An alternate constructive approach to the $\varphi ^4_3$ quantum field theory, and a possible destructive approach to $\varphi ^4_4$

Sokal, Alan D.

Annales de l'I.H.P. Physique théorique, Tome 37 (1982), p. 317-398 / Harvested from Numdam

Détail

Publié le : 1982-01-01

MR 693644 | 1 citation dans Numdam

Bibliographie

[1] J. Glimm and A. Jaffe, Positivity of the φ43 Hamiltonian. Fortsch. Physik, t. 21, 1973, p. 327-376. | MR 408581

[2] J. Feldman, The λφ43 theory in a finite volume. Commun. Math. Phys., t. 37, 1974, p. 93-120. | MR 384003

[3] J.S. Feldman and K. Osterwalder, The Wightman axioms and the mass gap for weakly coupled (φ4)3 quantum field theories. Ann. Phys., t. 97, 1976, p. 80-135. | MR 416337

[4] J. Magnen and R. Sénéor, The infinite volume limit of the φ43 model. Ann. Inst. Henri Poincaré, t. A 24, 1976, p. 95-159. | Numdam | MR 406217

[5] J. Magnen and R. Sénéor, Phase space cell expansion and Borel summability for the Euclidean φ43 theory. Commun. Math. Phys., t. 56, 1977, p. 237-276. | MR 523030

[5'] G. Gallavotti, Some aspects of the renormalization problems in statistical mechanics and field theory. Mem. Accad. Lincei, t. 15, 1978, p. 23-59. | MR 530273

[5''] G. Gallavotti, On the ultraviolet stability in statistical mechanics and field theory. Ann. Mat. Pura Appl., t. 120, 1979, p. 1-23. | MR 551060 | Zbl 0418.60098

[5'''] G. Benfatto, M. Cassandro, G. Gallavotti, F. Nicolò, E. Olivieri, E. Presutti and E. Scacciatelli, Some probabilistic techniques in field theory. Commun. Math. Phys., t. 59, 1978, p. 143-166. | MR 491611 | Zbl 0381.60096

[5''''] G. Benfatto, M. Cassandro, G. Gallavotti, F. Nicolò, E. Olivieri, E. Presutti and E. Scacciatelli, Ultraviolet stability in Euclidean scalar field theories. Commun. Math. Phys., t. 71, 1980, p. 95-130. | MR 560344 | Zbl 0427.60098

[6] B. Simon, The P(φ)2 Euclidean (quantum) field theory. Princeton, N. J., Princeton University Press, 1974. | MR 489552

[7] J. Rosen, Mass renormalization for the λφ4 Euclidean lattice field theory. Adv. Appl. Math., t. 1, 1980, p. 37-49. | MR 603124 | Zbl 0453.60097

[8] J. Glimm and A. Jaffe, Remark on the existence of φ44. Phys. Rev. Lett., t. 33, 1974, p. 440-442. | MR 400969

[9] G.A. Bakerjr., , Self-interacting, boson, quantum field theory and the thermodynamic limit in d dimensions. J. Math. Phys., t. 16, 1975, p. 1324-1346. | MR 395612

[10] F. Guerra, L. Rosen and B. Simon. The P(φ)2 Euclidean quantum field theory as classical statistical mechanics. Ann. Math., t. 101, 1975, p. 111-259. | MR 378670

[11] Y.M. Park, Convergence of lattice approximations and infinite volume limit in the (λφ4-σφ2-μφ)3 field theory. J. Math. Phys., t. 18, p. 354-366, 1977. | MR 432062

[12] R. Schrader, A possible constructive approach to φ44. I. Commun. Math. Phys., t. 49, 1976, p. 131-153, II. Ann. Inst. Henri Poincaré, t. A 26, 1977, p. 295-301, III. Commun. Math. Phys., t. 50, 1976, p. 97-102.

[13] K. Osterwalder and R. Schrader, Axioms for Euclidean Green's functions. I. Commun. Math. Phys., t. 31, 1973, p. 83-112. II. Commun. Math. Phys., t. 42, 1975, p. 281-305. | Zbl 0274.46047

[14] J. Glimm and A. Jaffe, Functional integral methods in quantum field theory. In: New developments in quantum field theory and statistical mechanics (1976 Cargèse lectures). M. Lévy and P. Mitter, eds., New York and London, Plenum Press, 1977. | MR 673947

[15] C.M. Newman, Inequalities for Ising models and field theories which obey the Lee-Yang theorem. Commun. Math. Phys., t. 41, 1975, p. 1-9. | MR 376061

[16] L.D. Landau, Collected papers of L. D. Landau (D. ter Haar, ed.), New York-London-Paris : Gordon and Breach, 1965. | MR 237287

[17] L. Landau, On the quantum theory of fields. In: Niels Bohr and the development of physics (W. Pauli, ed.), London, Pergamon Press, 1955. Reprinted in [16]. | MR 75092

[18] L. Landau and I. Pomeranchuk, On point interactions in quantum electrodynamics. Dokl. Akad. Nauk S. S. S. R., t. 102, 1955, p. 489-492. English translation in [16]. | MR 73476

[19] I. Pomerančuk, Vanishing of the renormalized charge in electrodynamics and in meson theory. Nuovo Cim., t. 3, 1956, p. 1186-1203. | MR 82373 | Zbl 0071.23101

[20] I. Ya. Pomeranchuk, V.V. Sudakov and K.A. Ter-Martirosyan, Vanishing of renormalized charges in field theories with point interaction. Phys. Rev., t. 103, 1956, p. 784-802. | MR 82374

[21] A.D. Galanin, On the possibility of formulating a meson theory with several fields. Zh. Eksp. Teor. Fiz., t. 32, 1957, p. 552-558 [Soviet Phys., J. E. T. P., t. 5, 1957, p. 460-464]. | MR 91813

[22] I.T. Diatlov, V.V. Sudakov and K.A. Ter-Martirosyan, Asymptotic mesonmeson scattering theory. Zh. Eksp. Teor. Fiz., t. 32, 1957, p. 767-780 [Soviet Phys., J. E. T. P., t. 5, 1957, p. 631-642]. | Zbl 0138.45802

[23] A.A. Abrikosov, A.D. Galanin, L.P. Gorkov, L.D. Landau, I. Ya. Pomeranchuk and K.A. Ter-Martirosyan, Possibility of formulation of a theory of strongly interacting fermions. Phys. Rev., t. 111, 1958, p. 321-328. Reprinted in [16]. | MR 135109 | Zbl 0082.44204

[24] E.S. Fradkin, The asymptote of Green's function in quantum electrodynamics. Zh. Eksp. Teor. Fiz., t. 28, 1955, p. 750-752 [Soviet Phys., J. E. T. P., t. 1, 1955, p. 604-606]. | Zbl 0067.21505

[25] E.S. Fradkin, The problem of the asymptote of the Green function in the theory of mesons with pseudoscalar coupling. Zh. Eksp. Teor. Fiz., t. 29, 1955, p. 377-379 [Soviet Phys., J. E. T. P., t. 2, 1956, p. 340-342]. | Zbl 0071.42901

[26] D.A. Kirzhnits, Contribution to field theory involving a cut-off factor. Zh. Eksp. Teor. Fiz., t. 32, 1957, p. 534-541 [Soviet Phys., J. E. T. P., t. 5, 1957, p. 445-451]. | MR 92602

[27] S. Kamefuchi, A comment on Landau's method of integration in quantum electrodynamics. Mat. Fys. Medd. Dan. Vid. Selsk., t. 31, 1957, no. 6. | MR 91787 | Zbl 0079.42704

[28] A.A. Ansel'M, Asymptotic theory of a one-dimensional four-fermion interaction. Zh. Eksp. Teor. Fiz., t. 35, 1958, p. 1522-1531 [Soviet Phys., J. E. T. P., t. 8, 1959, p. 1065-1071].

[29] N.N. Bogoliubov and D.V. Shirkov, Introduction to the theory of quantized fields. New York, Interscience, 1959, Chapter VIII, especially p. 528-529. | MR 110471 | Zbl 0088.21701

[30] J. Glimm and A. Jaffe, Particles and scaling for lattice fields and Ising models. Commun. Math. Phys., t. 51, 1976, p. 1-13. | MR 432054

[31] J. Bricmont, J.-R. Fontaine, J.L. Lebowitz and T. Spencer, Lattice systems with a continuous symmetry. II. Decay of correlations. Commun. Math. Phys., t. 78, 1981, p. 363-371. | MR 603499

[31'] J. Bricmont, J.-R. Fontaine, J.L. Lebowitz, E.H. Lieb and T. Spencer, Lattice systems with a continuous symmetry. III. Low temperature asymptotic expansion for the plane rotator model. Commun. Math. Phys., t. 78, 1981, p. 545-566. | MR 606463

[32] M.E. Fisher, Rigorous inequalities for critical-point correlation exponents. Phys. Rev., t. 180, 1969, p. 594-600.

[33] B. Simon, Functional integration and quantum physics. New York-San Francisco- London, Academic Press, 1979. | MR 544188 | Zbl 0434.28013

[34] E. Brézin, J.C. Leguillou and J. Zinn-Justin, Field theoretical approach to critical phenomena. In: Phase transitions and critical phenomena, t. 6. C. Domb and M. S. Green, eds., London-New York-San Francisco, Academic Press, 1976. | MR 495798

[35] K. Symanzik, Regularized quantum field theory. In: New developments in quantum field theory and statistical mechanics (1976 Cargèse Lectures). M. Lévy and P. Mitter, eds. New York and London, Plenum Press, 1977. | MR 522160

[36] K.G. Wilson, Quantum field-theory models in less than 4 dimensions. Phys. Rev., t. D 7, 1973, p. 2911-2926. | MR 386545

[37] R.B. Griffiths, Phase transitions. In: Statistical mechanics and quantum field theory (1970 Les Houches lectures). C. DeWitt and R. Stora, eds. New York-London- Paris, Gordon and Breach, 1971.

[38] G.S. Sylvester, Continuous-spin Ising ferromagnets. M. I. T. dissertation (mathematics), 1976.

[39] R.L. Dobrushin, The description of a random field by means of conditional probabilities and conditions of its regularity. Teor. Veroya. Prim., t. 13, 1968, p. 201- 229 [Theor. Prob. Appl., t. 13, 1968, p. 197-224]. | MR 231434 | Zbl 0184.40403

[40] R.L. Dobrushin, Gibbsian random fields for lattice systems with pairwise interactions. Funkts. Anal. Prilozh., t. 2, no. 4, 1968, p. 31-43 [Funct. Anal. Appl., t. 2, 1968, p. 292-301]. | MR 250630

[41] O.E. Lanford Iii and D. Ruelle, Observables at infinity and states with short range correlations in statistical mechanics. Commun. Math. Phys., t. 13, 1969, p. 194-215. | MR 256687

[42] C. Preston, Random fields. Lecture notes in mathematics # 534, Berlin-Heidelberg- New York, Springer-Verlag, 1976. | MR 448630 | Zbl 0335.60074

[43] M. Cassandro, E. Olivieri, A. Pellegrinotti and E. Presutti, Existence and uniqueness of DLR measures for unbounded spin systems. Z. Wahrscheinlichkeitstheorie verw. Gebiete, t. 41, 1978, p. 313-334. | MR 471115 | Zbl 0369.60116

[44] J.L. Lebowitz and E. Presutti, Statistical mechanics of systems of unbounded spins. Commun. Math. Phys., t. 50, 1976, p. 195-218 ; t. 78 (E), 1980, p. 151. | MR 446251

[45] G.S. Sylvester, Inequalities for continuous-spin Ising ferromagnets. J. Stat. Phys., t. 15, 1976, p. 327-341. | MR 436856

[46] C.M. Newman, Gaussian correlation inequalities for ferromagnets. Z. Wahrscheinlichkeitstheorie verw. Gebiete, t. 33, 1975, p. 75-93. | MR 398401 | Zbl 0297.60053

[47] G.S. Sylvester, Representations and inequalities for Ising model Ursell functions. Commun. Math. Phys., t. 42, 1975, p. 209-220. | MR 406301

[48] J. Bricmont, The Gaussian inequality for multicomponent rotators. J. Stat. Phys., t. 17, 1977, p. 289-300. | MR 462408

[49] G.A. Battle and L. Rosen, The FKG inequality for the Yukawa2 quantum field theory. J. Stat. Phys., t. 22, 1980, p. 123-192. | MR 560554

[50] C.M. Newman, Moment inequalities for ferromagnetic Gibbs distributions. J. Math. Phys., t. 16, 1975, p. 1956-1959. | MR 391853

[51] R. Schrader, New correlation inequalities for the Ising model and P(φ) theories. Phys. Rev., t. B 15, 1977, p. 2798-2803. | MR 449416

[52] A. Messager and S. Miracle-Sole, Correlation functions and boundary conditions in the Ising ferromagnet. J. Stat. Phys., t. 17, 1977, p. 245-262. | MR 676312

[53] G.C. Hegerfeldt, Correlation inequalities for Ising ferromagnets with symmetries. Commun. Math. Phys., t. 57, 1977, p. 259-266. | MR 503339

[54] D. Szàsz, Correlation inequalities for non-purely-ferromagnetic systems. J. Stat. Phys., t. 19, 1978, p. 453-459. | MR 515466

[55] J. Fröhlich, R. Israel, E.H. Lieb and B. Simon, Phase transitions and reflection positivity. I. General theory and long range lattice models. Commun. Math. Phys., t. 62, 1978, p. 1-34. | MR 506363

[56] R.S. Schor, The particle structure of v-dimensional Ising models at low temperatures. Commun. Math. Phys., t. 59, 1978, p. 213-233. | MR 484194

[57] A.D. Sokal, Representations and inequalities for the 2-point function in classical lattice systems. Unpublished manuscript, 1980.

[58] J. Fröhlich, B. Simon and T. Spencer, Infrared bounds, phase transitions and continuous symmetry breaking. Commun. Math. Phys., t. 50, 1976, p. 79-85. | MR 421531

[59] B. Simon, New rigorous existence theorems for phase transitions in model systems. In: Statistical Physics, « Statphys 13 » (1977 I. U. P. A. P. conference, Haifa), part 1, D. Cabib et al., eds. Annals of the Israel Physical Society, t. 2, 1978. | MR 513012

[60] B. Simon, Correlation inequalities and the mass gap in P(φ)2. I. Domination by the two point function. Commun. Math. Phys., t. 31, 1973, p. 127-136. | MR 329495

[61] A.D. Sokal, More inequalities for critical exponents. J. Stat. Phys., t. 25, 1981, p. 25-50. | MR 610690

[62] B. Simon, Decay of correlations in ferromagnets. Phys. Rev. Lett., t. 44, 1980, p. 547- 549. | MR 557644

[63] B. Simon, Correlation inequalities and the decay of correlations in ferromagnets. Commun. Math. Phys., t. 77, 1980, p. 111-126. | MR 589426

[64] J. Glimm and A. Jaffe, Three-particle structure of φ4 interactions and the scaling limit. Phys. Rev., t. D 11, 1975, p. 2816-2827. | MR 452301

[65] P.J. Paes-Leme, Ornstein-Zernike and analyticity properties for classical lattice spin systems. Ann. Phys., t. 115, 1978, p. 367-387. | MR 513891 | Zbl 0397.42011

[66] O.A. Mcbryan and J. Rosen, Existence of the critical point in φ4 field theory. Commun. Math. Phys., t. 51, 1976, p. 97-105. | MR 421428

[67] E.H. Lieb, A refinement of Simon's correlation inequality. Commun. Math. Phys., t. 77, 1980, p. 127-135. | MR 589427

[68] J. Glimm and A. Jaffe, Critical exponents and elementary partices. Commun. Math. Phys., t. 52, 1977, p. 203-209. | MR 443684

[69] A.D. Sokal, Unpublished, 1980.

[70] J.L. Lebowitz and A. Martin-Löf, On the uniqueness of the equilibrium state for Ising spin systems. Commun. Math. Phys., t. 25, 1972, p. 276-282. | MR 312854

[71] G.A. Baker Jr., B.G. Nickel, M.S. Green and D.I. Meiron, Ising-model critical indices in three dimensions from the Callan-Symanzik equation. Phys. Rev. Lett., t. 36, 1976, p. 1351-1354.

[72] J. Glimm and A. Jaffe, Absolute bounds on vertices and couplings. Ann. Inst. Henri Poincaré, t. A 22, 1975, p. 97-107. | Numdam | MR 384012

[73] R. Schrader, New rigorous inequality for critical exponents in the Ising model. Phys. Rev., t. B 14, 1976, p. 172-173. | MR 443769

[74] A.D. Sokal, Improved rigorous upper bound for the renormalized 4-point coupling. In preparation.

[75] D.G. Boulware and L.S. Brown, Tree graphs and classical fields. Phys. Rev., t. 172, 1968, p. 1628-1631.

[76] R.W. Johnson, Finite integral equations for Green's functions for :φ4: coupling. J. Math. Phys., t. 11, 1970, p. 2161-2165.

[77] M. Suzuki, Generalized exact formula for the correlations of the Ising model and other classical systems. Phys. Lett., t. 19, 1965, p. 267-268. | MR 187824 | Zbl 0129.23602

[78] F. Schwabl, Generating functional and Green's function hierarchy of the Ising model. Ann. Phys., t. 54, 1969, p. 1-16. | MR 250600

[79] H. Lehmann, K. Symanzik and W. Zimmermann, Zur Vertexfunktion in quantisierten Feldtheorien. Nuovo Cim., t. 2, 1955, p. 425-432. | MR 76638 | Zbl 0066.22604

[80] G. Barton, Introduction to advanced field theory. New York, Interscience, 1963, Chapters 10-12. | MR 159583 | Zbl 0116.44903

[81] K.W. Ford, Problem of ghost states in field theories. Phys. Rev., t. 105, 1957, p. 320- 327. | MR 82893 | Zbl 0077.42502

[82] E. Ferrari and G. Jona-Lasinio, Remarks on the appearance of ghost states in relativistic field theories. Nuovo Cim., t. 16, 1960, p. 867-885. | Zbl 0090.44705

[83] K. Symanzik, On the many-particle structure of Green's functions in quantum field theory. J. Math. Phys., t. 1, 1960, p. 249-273, Section 5 and Appendix B. | MR 145878

[84] L.E. Evans, High energy theorem in quantum electrodynamics. Nucl. Phys., t. 17, 1960, p. 163-168. | MR 121148

[85] J. Glimm and A. Jaffe, Critical exponents and renormalization in the φ4 scaling limit. In: Quantum dynamics, models and mathematics (1975 Bielefeld symposium), L. Streit, ed. Wien-New York, Springer-Verlag, 1976. Acta Physica Austriaca Suppl., t. XVI, 1976, p. 147-166. | MR 673762

[86] D. Marchesin, The scaling limit of the φ2 field in the anharmonic oscillator: existence and numerical studies. NYU preprint, 1978. | MR 531285

[87] A.D. Sokal, A rigorous inequality for the specific heat of an Ising or φ4 ferromagnet. Phys. Lett., t. 71 A, 1979, p. 451-453. | MR 588470

[88] A.S. Wightman, Should we believe in quantum field theory? In: The whys of subnuclear physics (1977 Erice lectures). A. Zichichi, ed. New York, Plenum Press, 1979.

[89] R.F. Streater and A.S. Wightman, PCT, spin and statistics, and all that. New York- Amsterdam, Benjamin, 1964. Second edition, 1978. | MR 468904 | Zbl 0135.44305

[90] G. Källén, Review of consistency problems in quantum electrodynamics. In: Quantum electrodynamics. P. Urban, ed., Wien-New York, Springer-Verlag, 1965. Acta Physica Austriaca Suppl., t. II, 1965, p. 133-161.

[91] K.G. Wilson, Renormalization group and strong interactions. Phys. Rev., t. D 3, 1971, p. 1818-1846. | MR 332009

[92] S. Coleman, Dilatations. In: Properties of the fundamental interactions (1971 Erice lectures), A. Zichichi, ed., Bologna, Editrice Compositori, 1973.

[93] D.J. Gross, Applications of the renormalization group to high-energy physics. In: Methods in field theory (1975 Les Houches lectures), R. Balian and J. Zinn-Justin, eds., Amsterdam-New York, North-Holland, 1976.

[94] K.G. Wilson and J. Kogut, The renormalization group and the ∈ expansion. Phys. Rep., t. 12, 1974, p. 75-200.

[94'] R.D. Pisarski, Fixed-point structure of (φ6)3 at large N. Phys. Rev. Lett., t. 48, 1982, p. 574-576. | MR 646742

[95] S.L. Adler, Short-distance behavior of quantum electrodynamics and an eigenvalue condition for α. Phys. Rev., t. D 5, 1972, p. 3021-3047; t. D 7, 1973, (E), p. 1948.

[96] K. Johnson and M. Baker, Some speculations on high-energy quantum electrodynamics. Phys. Rev., t. D 8, 1973, p. 1110-1122.

[97] B.M. Mccoy and T.T. Wu, Non-perturbative quantum field theory. Scientia Sinica, t. 22, 1979, p. 1021-1032. | MR 551136

[98] N.N. Khuri, Zeros of the Gell-Mann-Low function and Borel summations in renormalizable theories. Phys. Lett., t. 82 B, 1979, p. 83-88.

[99] C. Domb and M.S. Green, Phase transitions and critical phenomena. Vol. 3, Series expansions for lattice models. London-New York, Academic Press, 1974. | MR 353911

[100] H. Kunz, Analyticity and clustering properties of unbounded spin systems. Commun. Math. Phys., t. 59, 1978, p. 53-69. | MR 479235

[101] G.S. Sylvester, Weakly coupled Gibbs measures. Z. Wahrscheinlichkeitstheorie verw. Gebiete, t. 50, 1979, p. 97-118. | MR 550125 | Zbl 0402.60099

[102] J. Glimm, A. Jaffe and T. Spencer, The particle structure of the weakly coupled P(φ)2 model and other applications of high temperature expansions. Part II: The cluster expansion. In: Constructive quantum field theory (1973 Erice lectures), G. Velo and A. Wightman, eds., Berlin-Heidelberg-New York, Springer-Verlag, 1973. | MR 395513

[103] G.A. Bakerjr., , Essentials of Padé approximants. New York, Academic Press, 1975. | Zbl 0315.41014

[104] J.D. Bessis, J.M. Drouffe and P. Moussa, Positivity contraints for the Ising ferromagnetic model. J. Phys., t. A 9, 1976, p. 2105-2124.

[105] G.A. Bakerjr., and J.M. Kincaid, Continuous-spin Ising model and λ: φ4:d field theory. Phys. Rev. Lett., t. 42, 1979, p. 1431-1434; t. 44 (E), 1980, p. 434.

[106] G.A. Bakerjr., and J.M. Kincaid, The continuous-spin Ising model, g0 : ø4 :d field theory, and the renormalization group. J. Stat. Phys., t. 24, 1981, p. 469-528. | MR 607611

[107] G.A. Bakerjr., , Analysis of hyperscaling in the Ising model by the high-temperature series method. Phys. Rev., t. B 15, 1977, p. 1552-1559.

[108] D.S. Gaunt and M.F. Sykes, The critical exponent γ for the three-dimensional Ising model. J. Phys., t. A 12, 1979, L 25-L 28.

[109] S. Mckenzie, M.F. Sykes and D.S. Gaunt, The critical isotherm of the four-dimensional Ising model. J. Phys., t. A 12, 1979, p. 743-746.

[110] D.S. Gaunt, M.F. Sykes and S. Mckenzie, Susceptibility and fourth-field derivative of the spin-1/2 Ising model for T > Tc and d = 4. J. Phys., t. A 12, 1979, p. 871-877.

[111] S. Mckenzie, The exponent γ for the spin-1/2 Ising model on the face-centered cubic lattice. J. Phys., t. A 12, 1979, L 185-L 188.

[112] J. Oitmaa and J. Ho-Ting-Hun, The critical exponent y for the three-dimensional Ising model. J. Phys., t. A 12, 1979, L 281-L 282.

[113] B.G. Nickel and B. Sharpe, On hyperscaling in the Ising model in three dimensions. J. Phys., t. A 12, 1979, p. 1819-1834.

[114] J.J. Rehr, Confluent singularities and hyperscaling in the spin-1/2 Ising model. J. Phys., t. A 12, 1979, L 179-L 183.

[115] J. Zinn-Justin, Analysis of Ising model critical exponents from high temperature series expansion. J. de Physique, t. 40, 1979, p. 969-975.

[116] S. Mckenzie and D.S. Gaunt, A test of hyperscaling for the spin-1/2 Ising model in four dimensions. J. Phys., t. A 13, 1980, p. 1015-1021.

[117] D. Bessis, P. Moussa and G. Turchetti, Subdominant critical indices for the ferromagnetic susceptibility of the spin-1/2 Ising model. J. Phys., t. A 13, 1980, p. 2763-2773.

[118] B. Nickel, Hyperscaling and universality in 3 dimensions. Physica, t. 106 A, 1981, p. 48-58.

[119] B.G. Nickel, The problem of confluent singularities. In: Phase Transitions (1980 Cargèse lectures), M. Lévy, J.-C. LeGuillou and J. Zinn-Justin, eds., New York and London, Plenum Press, 1982.

[120] R. Roskies, Hyperscaling in the Ising model on the simple cubic lattice. Phys. Rev., t. B 23, 1981, p. 6037-6042.

[120'] J. Zinn-Justin, Analysis of high temperature series of the spin S Ising model on the body-centred cubic lattice. J. de Physique, t. 42, 1981, p. 783-792.

[120''] R.Z. Zoskies, Reconciliation of high temperature series and renormalization group results by suppressing confluent singularities. Phys. Rev., t. B 24, 1981, p. 5305-5317. | MR 643598

[121] M.E. Fisher, General scaling theory for critical points. In: Collective properties of physical systems (24th Nobel symposium). B. Lundqvist and S. Lundqvist, eds., Uppsala, Almqvist & Wiksell, 1974.

[122] D. Isaacson, The critical behavior of ø41. Commun. Math. Phys., t. 53, 1977, p. 257- 275. | MR 438956 | Zbl 0348.34016

[123] B.M. Mccoy, C.A. Tracy and T.T. Wu, Two-dimensional Ising model as an exactly soluble relativistic quantum field theory: explicit formulas for n-point functions. Phys. Rev. Lett., t. 38, 1977, p. 793-796.

[124] M.E. Fisher, The theory of equilibrium critical phenomena. Reports Prog. Phys., t. 30, 1967, p. 615-730.

[125] W.J. Camp, D.M. Saul, J.P. Vandyke and M. Wortis, Series analysis of corrections to scaling for the spin-pair correlations of the spin-s Ising model: confluent singularities, universality and hyperscaling. Phys. Rev., t. B 14, 1976, p. 3990-4001.

[126] T. Spencer, Private communication.

[127] C. Friedman, Perturbations of the Schrödinger equation by potentials with small support. J. Funct. Anal., t. 10, 1972, p. 346-360. | MR 340779 | Zbl 0235.35009

[128] K. Symanzik, Euclidean quantum field theory. I. Equations for a scalar model. J. Math. Phys., t. 7, 1966, p. 510-525. | MR 187686

[129] K. Symanzik, Euclidean quantum field theory. In: Local quantum theory (1968 Varenna lectures), R. Jost, ed., New York-London, Academic Press, 1969.

[130] D. Brydges and P. Federbush, A lower bound for the mass of a random Gaussian lattice. Commun. Math. Phys., t. 62, 1978, p. 79-82. | MR 496278 | Zbl 0381.60059

[131] A.J. Kupiainen, On the 1/n expansion. Commun. Math. Phys., t. 73, 1980, p. 273-294. | MR 574175

[131'] R.L. Wolpert, Wiener path intersections and local time. J. Funct. Anal., t. 30, 1978, p. 329-340. | MR 518339 | Zbl 0403.60069

[131''] R.L. Wolpert, Local time and a particle picture for Euclidean field theory. J. Funct. Anal., t. 30, 1978, p. 341-357. | MR 518340 | Zbl 0464.70016

[132] A. Dvoretzky, P. Erdös and S. Kakutani, Double points of paths of Brownian motion in n-space. Acta Sci. Math. (Szeged), t. 12 B, 1950, p. 75-81. | MR 34972 | Zbl 0036.09001

[133] M.J. Westwater, On Edwards' model for long polymer chains. Commun. Math. Phys., t. 72, 1980, p. 131-174. | MR 573702 | Zbl 0431.60100

[133'] J. Westwater, On Edwards' model for polymer chains. III. Borel summability. Commun. Math. Phys., t. 84, 1982, p. 459-470. | MR 667754 | Zbl 0498.60095

[134] G.F. Lawler, A self-avoiding random walk. Duke Math. J., t. 47, 1980, p. 655-693. | MR 587173 | Zbl 0445.60058

[135] S. Coleman, R. Jackiw and H.D. Politzer, Spontaneous symmetry breaking in the O(N) model for large N. Phys. Rev., t. D 10, 1974, p. 2491-2499.

[136] V.B. Berestetskiĭ, Zero-charge and asymptotic freedom. Usp. Fiz. Nauk, t. 120, 1976, p. 439-454 [Soviet Phys., Uspekhi, t. 19, 1976, p. 934-943].

[137] P. Olesen, On vacuum instability in quantum field theory. Phys. Lett., t. 73 B, 1978, p. 327-329.

[138] S. Coleman, Unpublished. Cited in [93].

[139] G. Feldman, Modified propagators in field theory (with application to the anomalous magnetic moment of the nucleon). Proc. Roy. Soc. (London), t. A 223, 1954, p. 112-129. | Zbl 0055.21507

[140] L.D. Landau, A.A. Abrikosov and I.M. Khalatnikov, An asymptotic expression for the photon Green function in quantum electrodynamics. Dokl. Akad. Nauk S. S. S. R., t. 95, 1954, p. 1177-1180. English translation in [16]. | MR 64655 | Zbl 0059.22001

[141] D.J. Gross and A. Neveu, Dynamical symmetry breaking in asymptotically free field theories. Phys. Rev., t. D 10, 1974, p. 3235-3253, Appendix.

[142] T.D. Lee, Some special examples in renormalizable field theory. Phys. Rev., t. 95, 1954, p. 1329-1334. | MR 64658 | Zbl 0058.23204

[143] G. Källén and W. Pauli, On the mathematical structure of T. D. Lee's model of a renormalizable field theory. Dan. Mat. Fys. Medd., t. 30, no. 7, 1955. | Zbl 0066.44301

[144] S.S. Schweber, An introduction to relativistic quantum field theory. Evanston, Illinois and Elmsford, New York, Row, Peterson and Co., 1961, Section 12b. | MR 127796 | Zbl 0111.43102

[145] A.A. Ansel'M, Solution of equation for the meson-meson scattering amplitude in the asymptotic region . Zh. Eksp. Teor. Fiz., t. 38, 1960, p. 1887-1890 [Soviet Phys., J. E. T. P., t. 11, 1960, p. 1356-1358]. | MR 121191

[146] T.T. Wu, Perturbation theory of pion-pion interaction. II. Two-pion approximation. Phys. Rev., t. 126, 1962, p. 2219-2226. | MR 140295 | Zbl 0109.45106

[147] A.B. Zamolodchikov, Yu.M. Makeenko and K.A. Ter-Martirosyan, A theory of direct four-fermion interactions. Zh. Eksp. Teor. Fiz., t. 71, 1976, p. 24-45 [Soviet Phys., J. E. T. P., t. 44, 1976, p. 11-22].

[148] A.I. Larkin and D.E. Khmel'Nitksiĭ, Phase transition in uniaxial ferroelectrics. Zh. Eksp. Teor. Fiz., t. 56, 1969, p. 2087-2098 [Soviet Phys., J. E. T. P., t. 29, 1969, p. 1123-1128].

[149] A.M. Polyakov, Properties of long and short range correlations in the critical region. Zh. Eksp. Teor. Fiz., t. 57, 1969, p. 271-283 [Soviet Phys., J. E. T. P., t. 30, 1970, p. 151-157].

[150] K. Symanzik, Infrared singularities and small-distance-behaviour analysis. Commun. Math. Phys., t. 34, 1973, p. 7-36.

[151] T. Tsuneto and E. Abrahams, Skeleton graph expansion for critical exponents. Phys. Rev. Lett., t. 30, 1973, p. 217-220.

[152] S.L. Ginzburg, Vertex functions and Green functions in the (4-∈)-dimensional theory of phase transitions. Zh. Eksp. Teor. Fiz., t. 66, 1974, p. 647-654 [Soviet Phys., J. E. T. P., t. 39, 1974, p. 312-315].

[153] A.A. Abrikosov, Electron scattering on magnetic impurities in metals and anomalous resistivity effects. Physics, t. 2, 1965, p. 5-37.

[154] Yu.A. Bychkov, L.P. Gor'Kov and I.E. Dzyaloshinskiĭ, Possibility of superconductivity type phenomena in a one-dimensional system. Zh. Eksp. Teor. Fiz., t. 50, 1960, p. 738-758 [Soviet Phys., J. E. T. P., t. 23, 1966, p. 489-501].

[155] B. Roulet, J. Gavoret and P. Nozières, Singularities in the X-ray absorption and emission of metals. I. First-order parquet calculation. Phys. Rev., t. 178, 1969, p. 1072-1083.

[156] P. Nozières, J. Gavoret and B. Roulet, Singularities in the X-ray absorption and emission of metals. II. Self-consistent treatment of divergences. Phys. Rev., t. 178, 1969, p. 1084-1096.

[157] E.C. Poggio, On the renormalization method: a different outlook, and the energy-momentum tensor in the gφ4 theory. Ann. Phys., t. 81, 1973, p. 481-518.

[158] R.W. Haymaker and R. Blankenbecler, Variational principles for crossing-symmetric off-shell equations. Phys. Rev., t. 171, 1968, p. 1581-1587.

[159] R.J. Yaes, Nonassociativity of the operators in the crossing-symmetric Bethe-Salpeter equations. Phys. Rev., t. D 2, 1970, p. 2457-2463.

[160] W. Becker and D. Grosser, Crossing and unitarity in the context of the Bethe-Salpeter equation. Nuovo Cim., t. 10 A, 1972, p. 343-361.

[161] R.G. Root, Effective potential for the O(N) model to order 1/N. Phys. Rev., t. D 10, 1974, p. 3322-3334.

[162] G. Feinberg and A. Pais, A field theory of weak interactions. I. Phys. Rev., t. 131, 1963, p. 2724-2761. II. Phys. Rev., t. 133, 1964, B 477-B 486. | MR 156615 | Zbl 0121.22403

[163] B.A. Arbuzov and A.T. Filippov, Vertex function in nonrenormalizable field theory. Nuovo Cim., t. 38, 1965, p. 796-806. | MR 191350

[164] B.A. Arbuzov and A.T. Filippov, Iteration method in nonrenormalizable field theory. Zh. Eksp. Teor. Fiz., t. 49, 1965, p. 990-999 [Soviet Phys., J. E. T. P., t. 32, 1966, p. 688-693]. | MR 193957

[165] W. Güttinger, R. Penzl and E. Pfaffelhuber, Peratization of unrenormalizable field theories. Ann. Phys., t. 33, 1965, p. 246-271. | MR 189526

[166] T.D. Lee, Analysis of divergences in a neutral-spin-1-meson theory with parity-nonconserving interactions. Nuovo Cim., t. 59 A, 1969, p. 579-598.

[167] M.K. Volkov, Methods of quantum field theory with rapidly increasing spectral functions. Fortsch. Physik, t. 19, 1971, p. 757-782.

[168] L. Nitti, M.F. Pellicoro and M. Villani, Higher-order corrections in nonrenormalizable quantum field theories. Lett. Nuovo Cim., t. 3, 1972, p. 541-547.

[169] N.N. Khuri and A. Pais, Singular potentials and peratization. I. Rev. Mod. Phys., t. 36, 1964, p. 590-595. | MR 163673 | Zbl 0128.45604

[170] W.M. Frank, D.J. Land and R.M. Spector, Singular potentials. Rev. Mod. Phys., t. 43, 1971, p. 36-98. | MR 449255

[171] T.T. Wu, Theory of Toeplitz determinants and the spin correlations of the two-dimensional Ising model. I. Phys. Rev., t. 149, 1966, p. 380-401, Section 8(H).

[172] A.A. Slavuov and A.E. Shabad, Elimination of unphysical singularities in the Feinberg-Pais theory of weak interactions. Yad. Fiz., t. 1, 1965, p. 721-728 [Sov. J. Nucl. Phys., t. 1, 1965, p. 514-519].

[173] M.B. Halpern, Nonrenormalizable field theories. Ann. Phys., t. 39, 1966, p. 351-375.

[174] V.Sh. Gogokhiya and A.T. Filippov, Approximate methods for solving the Schrödinger equation with a singular potential. Yad. Fiz., t. 15, 1972, p. 1294-1306 [Sov. J. Nucl. Phys., t. 15, 1972, p. 714-719]. | MR 418696

[175] G. Parisi, The theory of non-renormalizable interactions. The large N expansion. Nucl. Phys., t. B 100, 1975, p. 368-388.

[176] J.C. Taylor, The form of the divergencies in quantum electrodynamics. Proc. Roy. Soc. (London), t. 234 A, 1956, p. 296-300. | MR 75826 | Zbl 0073.44802

[177] J.C. Taylor, Renormalization in meson theories. Proc. Camb. Philos. Soc., t. 52, 1956, p. 534-537. | MR 81176 | Zbl 0075.22103

[178] K.A. Ter-Martirosian, Charge renormalization for an arbitrary, not necessarily small, value of e0. Zh. Eksp. Teor. Fiz., t. 31, 1956, p. 157-159 [Soviet Phys., J. E. T. P., t. 4, 1957, p. 443-444]. | Zbl 0078.44503

[179] H.D. Politzer, Asymptotic freedom: An approach to the strong interactions. Phys. Rep., t. 14, 1974, p. 129-180.

[180] E.S. Fradkin and O.K. Kalashnikov, Renormalized set of equations for the Green functions in the Yang-Mills field theory and its asymptotic solution. J. Phys., t. A 9, 1976, p. 159-168.

[181] J.C. Collins and A.J. Macfarlane, New methods for the renormalization group. Phys. Rev., t. D 10, 1974, p. 1201-1212.

[182] K.G. Wilson, Renormalization group and critical phenomena. I. Renormalization group and the Kadanoff scaling picture. Phys. Rev., t. B 4, 1971, p.3174-3183. II. Phase-space cell analysis of critical behavior. Phys. Rev., t. B 4, 1971, p. 3184- 3205. | Zbl 1236.82017

[183] L.P. Kadanoff, A. Houghton and M.C. Yalabik, Variational approximations for renormalization group transformations. J. Stat. Phys., t. 14, 1976, p. 171-203; t. 15 (E), 1976, p. 263. | MR 456229

[184] H.W.J. Blöte and R.H. Swendsen, Critical behavior of the four-dimensional Ising model. Phys. Rev., t. B 22, 1980, p. 4481-4483. | MR 590597

[185] B. Simon, Coupling constant analyticity for the anharmonic oscillator. Ann. Phys., t. 58, 1970, p. 76-136. | MR 416322

[186] S. Graffi, V. Grecchi and B. Simon, Borel summability: application to the anharmonic oscillator. Phys. Lett., t. 32 B, 1970, p. 631-634. | MR 332068

[187] G. Parisi, The perturbative expansion and the infinite coupling limit. Phys. Lett., t. 69 B, 1977, p. 329-331.

[188] G.A. Bakerjr., , B.G. Nickel and D.I. Meiron, Critical indices from perturbation analysis of the Callan-Symanzik equation. Phys. Rev., t. B 17, 1978, p. 1365-1374.

[189] J.C. Leguillou and J. Zinn-Justin, Critical exponents for the n-vector model in three dimensions from field theory. Phys. Rev. Lett., t. 39, 1977, p. 95-98.

[190] J.C. Leguillou and J. Zinn-Justin, Critical exponents from field theory. Phys. Rev., t. B 21, 1980, p. 3976-3998. | MR 568441 | Zbl 0978.82507

[191] A.A. Vladimirov, Methods of calculating many-loop diagrams and renormalization-group analysis of the φ4 theory. Teor. Mat. Fiz., t. 36, 1978, p. 271-278 [Theor. Math. Phys., t. 36, 1978, p. 732-737]. | MR 507846

[192] F.M. Dittes, Yu.A. Kubyshin and O.V. Tarasov, Four-loop approximation in the φ4 model. Teor. Mat. Fiz., t. 37, 1978, p. 66-73 [Theor. Math. Phys., t. 37, 1978, p. 879-884]. | MR 514137

[193] N.N. Khuri, Solutions of the Callan-Symanzik equation in a complex neighborhood of zero coupling. Phys. Rev., t. D 12, 1975, p. 2298-2310. | MR 503199

[194] N.N. Khuri, Borel summability and the renormalization group. Phys. Rev., t. D 16, 1977, p. 1754-1761. | MR 452283

[195] A.D. Sokal, An improvement of Watson's theorem on Borel summability. J. Math. Phys., t. 21, 1980, p. 261-263. | MR 558468 | Zbl 0441.40012

[196] J. Zinn-Justin, Asymptotic estimate of perturbation theory at large orders. In: Hadron structure and lepton-hadron interactions (1977 Cargèse lectures). M. Lévy et al., eds., New York-London, Plenum Press, 1979. | MR 563276

[197] G. Parisi, The physical basis of asymptotic estimates in perturbation theory. In: Hadron structure and lepton-hadron interactions (1977 Cargèse lectures). M. Lévy et al., eds., New York-London, Plenum Press, 1979. | MR 563277

[198] L.D. Landau, Fundamental problems. In: Theoretical physics in the twentieth century, a memorial volume to Wolfgang Pauli, M. Fierz and V. F. Weisskopf, eds., New York, Interscience, 1960. Reprinted in [16]. | MR 115662 | Zbl 0094.36503

[199] D.B. Abraham and H. Kunz, Ornstein-Zernike theory of classical fluids at low density. Phys. Rev. Lett., t. 39, 1977, p. 1011-1014. | MR 452115

[200] G.A. Bakerjr., and D. Bessis, Asymptotic decay of correlations in the spin-1/2 Ising model. J. Math. Phys., t. 22, 1981, p. 1264-1266. | MR 621273

[201] C.M. Bender, G.S. Guralnik, R.W. Keener and K. Olaussen, Numerical study of truncated Green's-function equations. Phys. Rev., t. D 14, 1976, p. 2590-2595.

[202] B. Schroer, A necessary and sufficient condition for the softness of the trace of the energy-momentum tensor. Lett. Nuovo Cim., t. 2, 1971, p. 867-872.

[203] J.C. Collins, Renormalization of the energy-momentum tensor in φ4 theory. Phys. Rev., t. D 14, 1976, p. 1965-1976. | MR 421472

[204] E.C. Poggio, Short-distance behavior of a gφ4 theory, and conformal-invariant four-point functions. Phys. Rev., t. D 8, 1973, p. 2431-2446.

[205] V.K. Dobrev, G. Mack, V.B. Petkova, S.G. Petrova and I.T. Todorov, Harmonic analysis on the n-dimensional Lorentz group and its application to conformal quantum field theory (Lecture notes in physics # 63), Berlin-Heidelberg-New York, Springer-Verlag, 1977. | Zbl 0407.43010

[206] B. Geyer, V.A. Matveev, D. Robaschik and E. Wieczorek, Analytical properties of conformal invariant four point functions. Rep. Math. Phys., t. 10, 1976, p. 203- 211. | MR 573222 | Zbl 0345.32008

[207] G. Mack and I.T. Todorov, Conformal-invariant Green functions without ultraviolet divergences. Phys. Rev., t. D 8, 1973, p. 1764-1787.

[208] E.S. Fradkin and M.Ya. Palchik, Conformally invariant solution of quantum field theory equations (1). Nucl. Phys., t. B 99, 1975, p. 317-345.

[209] V.K. Dobrev, V.B. Petkova, S.G. Petrova and I.T. Todorov, Dynamical derivation of vacuum operator-product expansion in Euclidean conformal quantum field theory. Phys. Rev., t. D 13, 1976, p. 887-912.

[210] G. Mack, Osterwalder-Schrader positivity in conformal invariant quantum field theory. In: Trends in elementary particle theory (Lecture notes in physics # 37). H. Rollnik and K. Dietz, eds., Berlin-Heidelberg-New York, Springer-Verlag, 1975.

[211] R.A. Willoughby, The inverse M-matrix problem. Lin. Alg. Appl., t. 18, 1977, p. 75-94. | MR 472874 | Zbl 0355.15006

[212] T.L. Markham, Nonnegative matrices whose inverses are M-matrices. Proc. Amer. Math. Soc., t. 36, 1972, p. 326-330. | MR 309970 | Zbl 0281.15016

[213] B.B. Murphy, On the inverses of M-matrices. Proc. Amer. Math. Soc., t. 62, 1977, p. 196-198. | MR 429944 | Zbl 0322.15010

[214] G. Caginalp, The φ4 lattice field theory as an asymptotic expansion about the Ising limit. Ann. Phys., t. 124, 1980, p. 189-207. | MR 558098

[215] G. Caginalp, Thermodynamic properties of the φ4 lattice field theory near the Ising limit. Ann. Phys., t. 126, 1980, p. 500-511. | MR 576418

[216] F. Constantinescu, Strong-coupling expansion of the continuous-spin Ising model. Phys. Rev. Lett., t. 43, 1979, p. 1632-1635.

[217] L.H. Karsten and J. Smit, The vacuum polarization with SLAC lattice fermions. Phys. Lett., t. 85 B, 1979, p. 100-102.

[217'] J.M. Rabin, Long-range interactions in lattice field theory. SLAC-Report 240, June 1981.

[218] H.S. Sharatchandra, Continuum limit of lattice gauge theories in the context of renormalized perturbation theory. Phys. Rev., t. D 18, 1978, p. 2042-2055.

[218'] N. Kimura and A. Ukawa, Energy-momentum dispersion of glueballs and the restoration of Lorentz invariance in lattice gauge theories. Nucl. Phys., t. B 205 [FS5], 1982, p. 637-647.

[218''] C.B. Lang and C. Rebbi, Potential and restoration of rotational symmetry in SU(2) lattice gauge theory. Phys. Lett., t. 115 B, 1982, p. 137-142. | MR 669454

[219] R.F. Streater, Connection between the spectrum condition and the Lorentz invariance of P(φ)2. Commun. Math. Phys., t. 26, 1972, p. 109-120. | MR 297266

[220] E.P. Heifets and E.P. Osipov, The energy-momentum spectrum in the P(φ)2 quantum field theory. Commun. Math. Phys., t. 56, 1977, p. 161-172. | MR 489513 | Zbl 1155.82303

[221] A.D. Sokal, Unpublished, 1980.

[222] M. Reed and B. Simon, Methods of modern mathematical physics. III. Scattering theory, New York-San Francisco-London, Academic Press, 1979. | MR 529429 | Zbl 0405.47007

[223] A.D. Sokal, Unpublished, 1980.

[224] L. Monroe and P.A. Pearce, Correlation inequalities for vector spin models. J. Stat. Phys., t. 21, 1979, p. 615-633. | MR 555916

[225] M. Reed and B. Simon, Methods of modern mathematical physics. II. Fourier analysis, self-adjointness, New York-San Francisco-London, Academic Press, 1975. | MR 493420 | Zbl 0308.47002

[226] H.E. Stanley, Introduction to phase transitions and critical phenomena, New York, Oxford University Press, 1971.

[227] J. Glimm and A. Jaffe, ø42 quantum field model in the single-phase region: differentiability of the mass and bounds on critical exponents. Phys. Rev., t. D 10, 1974, p. 536-539.

[228] G.A. Baker, Jr., Critical exponent inequalities and the continuity of the inverse range of correlation. Phys. Rev. Lett., t. 34, 1975, p. 268-270.

[229] M. Aizenman, Proof of the triviality of φ4d field theory and some mean-field features of Ising models for d > 4. Phys. Rev. Lett., t. 47, 1981, p. 1-4, 886 (E). | MR 620135

[230] M. Aizenman, Geometric analysis of φ4 fields and Ising models (parts I and II). Commun. Math. Phys., t. 86, 1982, p. 1-48. | MR 678000 | Zbl 0533.58034

[231] J. Fröhlich, On the triviality of λφ4d theories and the approach to the critical point in d ≥ 4 dimensions. Nucl. Phys., t. B 200 [FS4], 1982, p. 281-296. | MR 643591

[232] D. Brydges, J. Fröhlich and T. Spencer, The random walk representation of classical spin systems and correlation inequalities. Commun. Math. Phys., t. 83, 1982, p. 123-150. | MR 648362

[233] D.C. Brydges, J. Fröhlich and A.D. Sokal, The random-walk representation of classical spin systems and correlation inequalities. II. The skeleton inequalities. Courant Institute preprint. | MR 719815

[234] D.C. Brydges, J. Fröhlich and A.D. Sokal, A new proof of the existence and nontriviality of the continuum φ42 and φ43 quantum field theories. Courant Institute preprint.

[235] R. Schrader and E. Tränkle, Analytic and numerical evidence from quantum field theory for the hyperscaling relation dv = 2Δ - γ in the d = 3 Ising model. J. Stat. Phys., t. 25, 1981, p. 269-290. | MR 624747

[236] K. Osterwalder, Unpublished, cited in [235, section 1].

[237] W. Driessler and J. Fröhlich, The reconstruction of local observable algebras from the Euclidean Green's functions of relativistic quantum field theory. Ann. Inst. Henri Poincaré, t. A 27, 1977, p. 221-236. | Numdam | MR 484123 | Zbl 0364.46051

[238] J.-P. Eckmann and H. Epstein, Time-ordered products and Schwinger functions. Commun. Math. Phys., t. 64, 1979, p. 95-130. | MR 519920

[239] A.D. Sokal, Mean-field bounds and correlation inequalities. J. Stat. Phys., t. 28, 1982, p. 431-439. | MR 668133