The large-scale limit of Dyson's hierarchical vector-valued model at low temperatures. The non-gaussian case. Part II : description of the large-scale limit
Bleher, P. M. ; Major, P.
Annales de l'I.H.P. Physique théorique, Tome 49 (1988), p. 87-143 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1988-01-01
@article{AIHPA_1988__49_1_87_0,
     author = {Bleher, Pavel M. and Major, P.},
     title = {The large-scale limit of Dyson's hierarchical vector-valued model at low temperatures. The non-gaussian case. Part II : description of the large-scale limit},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {49},
     year = {1988},
     pages = {87-143},
     mrnumber = {974869},
     zbl = {0669.60096},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1988__49_1_87_0}
}

Bleher, P. M.; Major, P. The large-scale limit of Dyson's hierarchical vector-valued model at low temperatures. The non-gaussian case. Part II : description of the large-scale limit. Annales de l'I.H.P. Physique théorique, Tome 49 (1988) pp. 87-143. http://gdmltest.u-ga.fr/item/AIHPA_1988__49_1_87_0/

[1] M. Aizenman, J.T. Chayes, L. Chayes, C.M. Newman, Discontinuity of the magnetization in one-dimensional 1/|x - y|2 Ising and Potts models. J. Stat. Phys., t. 50, 1988, p. 1-40. | MR 939480 | Zbl 01397676

[2] M. Aizenman, C.M. Newman, Discontinuity of the percolation density in one-dimensional 1/|x - y|2 percolation models. Commun. Math. Phys., t. 107, 1986, p. 611-647. | MR 868738 | Zbl 0613.60097

[3] P. Billingsley, Convergence of probability measures. Wiley, 1968. | MR 233396 | Zbl 0172.21201

[4] P.M. Bleher, Construction of non-Gaussian self-similar random fields with hierarchical structure. Commun. Math. Phys., t. 87, 1982, p. 226-240. | MR 667761 | Zbl 0515.60058

[5] P.M. Bleher, P. Major, Renormalization of Dyson's hierarchical vector-valued Φ4-model at low temperatures. Commun. Math. Phys., t. 95, 1984, p. 487-532. | MR 767191 | Zbl 0587.60098

[6] P.M. Bleher, P. Major, Critical phenomena and universal exponents in statistical physics. On Dyson's hierarchical model. The Annals of Probability, t. 15, 1987, p. 431-477. | MR 885127 | Zbl 0628.60101

[7] P.M. Bleher, P. Major, Limit theorems in statistical physics; On Dyson's hierarchical model. In the conference volume of the first world conference of the Bernoulli Society. | Zbl 0684.60082

[8] P.M. Bleher, Ya. G. Sinai, Investigation of the critical point in models of the type of Dyson's hierarchical model. Commun. Math. Phys., t. 33, 1973, p. 23-42.

[9] P.M. Bleher, Ya.G. Sinai, Critical indices for Dyson's asymptotically hierarchical models. Commun. Math. Phys., t. 45, 1975, p. 247-278.

[10] R.L. Dobrushin, Definition of random variables by conditional distributions. Teor. Veroyatn. Primen, t. 15, 1970, p. 469-497. | MR 298716 | Zbl 0264.60037

[11] R.L. Dobrushin, Gaussian and their subordinated self-similar fields. Annals of Probability, t. 7, 1979, p. 1-28. | MR 515810 | Zbl 0392.60039

[12] F.J. Dyson, Existence of phase transition in a one-dimensional Ising ferromagnet. Commun. Math. Phys., t. 42, 1969, p. 31-40. | MR 436850

[13] F.J. Dyson, An Ising ferromagnet with discontinuous long range order. Commun. Math. Phys., t. 21, 1971, p. 269-283. | MR 295719

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

[15] J. Fröhlich, T. Spencer, The Kosterlitz-Thouless transition in two-dimensional Abelian spin system and the Coulomb gas. Commun. Math. Phys., t. 81, 1981, p. 527-602. | MR 634447

[16] P. Major, Multiple Wiener-Itô integrals with applications to limit theorems. Lecture Notes in Mathematics, 849, Springer, 1981. | MR 611334 | Zbl 0451.60002

[17] C.M. Newman, L.S. Schulman, One-dimensional 1/|j - i|s percolation models; The existence of a transition for s ≤ 2. Commun. Math. Phys., t. 104, 1986, p. 547-571. | MR 841669 | Zbl 0604.60097

[18] A.M. Polyakov, Interaction of Goldstone particles in two dimensions. Applications to ferromagnets and massive Yang-Mills fields. Phys. Lett., t. 59 B, n° 1, 1975, p. 79-81.

[19] C.J. Preston, Gibbs states on countable sets. Cambridge Tracts, 68 Cambridge University Press, London, 1974. | MR 474556 | Zbl 0297.60054

[20] Ya.G. Sinai, Theory of phase transitions. Rigorous results. Pergamon, New York, 1982. | MR 691854 | Zbl 0537.60097

[21] K.G. Wilson, J. Kogut, The renormalization group and the ∈-expansion. Phys. Rept., t. 12 C, 2, 1974, p. 75-199.

[22] A. Patrascioiu, E. Seiler, A different perspective of the Kosterlitz-Thouless phase transition, to appear in Phys. Rev. Lett. | MR 932173

[23] V. Linke, A. Patrascioiu, E. Seiler, I.O. Stamatescu, Critical behaviour, scaling and universality in some two dimensional spin models, working paper, 1987.