Glauber dynamics of spin glasses at low and high temperature
De Santis, Emilio
Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002), p. 681-710 / Harvested from Numdam
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Publié le : 2002-01-01
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     author = {De Santis, Emilio},
     title = {Glauber dynamics of spin glasses at low and high temperature},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {38},
     year = {2002},
     pages = {681-710},
     mrnumber = {1931583},
     zbl = {1034.82051},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2002__38_5_681_0}
}

De Santis, Emilio. Glauber dynamics of spin glasses at low and high temperature. Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002) pp. 681-710. http://gdmltest.u-ga.fr/item/AIHPB_2002__38_5_681_0/

[1] M. Aizenman, R. Holley, Rapid convergence to equilibrium of stochastic Ising models in the Dobrushin Shlosman regime, in: Percolation Theory and Ergodic Theory of Infinite Particle Systems (Minneapolis, Minn., 1984-1985), IMA Vol. Math. Appl., 8, Springer, New York, 1987, pp. 1-11. | Zbl 0621.60118

[2] F. Cesi, C. Maes, F. Martinelli, Relaxation in disordered magnets in the Griffiths regime, Comm. Math. Phys. 188 (1) (1997) 135-173. | MR 1471335 | Zbl 0882.60095

[3] L. Chayes, J. Machta, Graphical representations and cluster algorithms. Part I: Discrete spin system, Phys. A 239 (1997) 542-601.

[4] E. De Santis, Swendsen-Wang dynamics on Zd for disordered non-ferromagnetic systems, Preprint.

[5] E. De Santis, A. Gandolfi, Bond percolation in frustrated systems, Ann. Probab. 27 (4) (1999) 1781-1808. | MR 1742888 | Zbl 0968.60092

[6] R. Diestel, Graph Theory, Springer-Verlag, Berlin, 1997. | MR 1448665 | Zbl 0859.05001

[7] P. Diaconis, D. Stroock, Geometric bounds for eigenvalues of Markov chains, Ann. Appl. Probab. 1 (1) (1991) 36-61. | MR 1097463 | Zbl 0731.60061

[8] R. Dobrushin, The description of a random field by means of conditional probabilities and conditions of its regularities, Theory Probab. Appl. 13 (1968) 197-224. | Zbl 0184.40403

[9] S. Edwards, P. Anderson, Theory of spin glasses, J. Phys. F 5 (1975) 965-974.

[10] J.A. Fill, Eigenvalue bounds on the convergence to stationarity for nonreversible Markov chains, with an application to the exclusion process, Ann. Appl. Probab. 1 (1) (1991) 62-87. | MR 1097464 | Zbl 0726.60069

[11] L. Fontes, M. Isopi, Y. Kohayakawa, P. Picco, The spectral gap of the REM under Metropolis Dynamics, Ann. Appl. Probab. 8 (3) (1998) 917-943. | MR 1627811 | Zbl 0935.60084

[12] G. Gallavotti, A. Martin-Löf, S. Miracle-Solé, Some problems connected with the description of coexisting phases at low temperatures in the Ising model, Statistical Mechanics and Mathematical Problems, Battelle Seattle 1971 Rencontres, 1971, p. 162.

[13] A. Gandolfi, C.M. Newman, D.L. Stein, Zero-temperature dynamics of ±J spin glasses and related models, Comm. Math. Phys. 214 (2000) 373-387. | MR 1796026 | Zbl 0978.82098

[14] G. Gielis, C. Maes, Percolation techniques in disordered spin flip dynamics: Relaxation to the unique invariant measure, Comm. Math. Phys. 177 (1) (1996) 83-101. | MR 1382221 | Zbl 0851.60096

[15] R.J. Glauber, Time dependent statistics of the Ising model, J. Math. Phys. 4 (1963) 294-307. | MR 148410 | Zbl 0145.24003

[16] R. Griffiths, Non-analytic behavior above the critical point in a random Ising ferromagnet, Phys. Rev. Lett. 23 (1969) 17-19.

[17] H. Kesten, Percolation Theory for Mathematicians, Progress in Probability and Statistics, Birkhäuser, 1982. | MR 692943 | Zbl 0522.60097

[18] O. Lanford, D. Ruelle, Observables at infinity and states with short range correlations in statistical mechanics, Comm. Math. Phys. 13 (1969) 194-215. | MR 256687

[19] T. Liggett, Interacting Particle Systems, Springer-Verlag, Berlin, 1985. | MR 776231 | Zbl 0559.60078

[20] S.L. Lu, H.T. Yau, Spectral gap logarithmic Sobolev inequality for Kawasaki and Glauber dynamics, Comm. Math. Phys. 156 (2) (1993) 399-433. | MR 1233852 | Zbl 0779.60078

[21] F. Martinelli, E. Olivieri, Approach to equilibrium of Glauber dynamics in the one phase region I. The attractive case, Comm. Math. Phys. 161 (3) (1994) 447-486. | MR 1269387 | Zbl 0793.60110

[22] F. Martinelli, E. Olivieri, Approach to equilibrium of Glauber dynamics in the one phase region II. The general case, Comm. Math. Phys. 161 (3) (1994) 487-514. | MR 1269388 | Zbl 0793.60111

[23] F. Martinelli, E. Olivieri, R.H. Schonmann, Systems weak mixing implies strong mixing, Comm. Math. Phys. 165 (1) (1994) 33-47. | MR 1298940 | Zbl 0811.60097

[24] F. Martinelli, E. Olivieri, E. Scoppola, On the Swendsen-Wang dynamics. II. Critical droplets and homogeneous nucleation at low temperature for the two-dimensional Ising Model, J. Statist. Phys. 62 (1-2) (1991) 135-159. | Zbl 0739.60098

[25] C.M. Newman, D.L. Stein, Zero-temperature dynamics of Ising spin systems following a deep quench: results and open problems, Phys. A 279 (2000) 159-168. | MR 1797138

[26] R. Swendsen, J. Wang, Nonuniversal critical dynamics in Monte Carlo simulations, Phys. Rev. Lett. 58 (86) (1987) 86-88.

[27] L.E. Thomas, Bound on the mass gap for finite volume stochastic Ising models at low temperature, Comm. Math. Phys. 126 (1) (1989) 1-11. | MR 1027910 | Zbl 0679.60102

[28] D.W. Stroock, B. Zegarlinski, The logarithmic Sobolev inequality for discrete spin systems on a lattice, Comm. Math. Phys. 149 (1) (1992) 175-193. | MR 1182416 | Zbl 0758.60070

[29] B. Zegarlinski, On log-Sobolev inequalities for infinite lattice systems, Lett. Math. Phys. 20 (3) (1990) 173-182. | MR 1074698 | Zbl 0717.47015