Glauber dynamics of spin glasses at low and high temperature
Annales de l'I.H.P. Probabilités et statistiques (2002)
- Volume: 38, Issue: 5, page 681-710
- ISSN: 0246-0203
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topDe Santis, Emilio. "Glauber dynamics of spin glasses at low and high temperature." Annales de l'I.H.P. Probabilités et statistiques 38.5 (2002): 681-710. <http://eudml.org/doc/77729>.
@article{DeSantis2002,
author = {De Santis, Emilio},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {spin glass; Ising model; Glauber dynamics},
language = {eng},
number = {5},
pages = {681-710},
publisher = {Elsevier},
title = {Glauber dynamics of spin glasses at low and high temperature},
url = {http://eudml.org/doc/77729},
volume = {38},
year = {2002},
}
TY - JOUR
AU - De Santis, Emilio
TI - Glauber dynamics of spin glasses at low and high temperature
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2002
PB - Elsevier
VL - 38
IS - 5
SP - 681
EP - 710
LA - eng
KW - spin glass; Ising model; Glauber dynamics
UR - http://eudml.org/doc/77729
ER -
References
top- [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. Zbl0621.60118
- [2] F. Cesi, C. Maes, F. Martinelli, Relaxation in disordered magnets in the Griffiths regime, Comm. Math. Phys.188 (1) (1997) 135-173. Zbl0882.60095MR1471335
- [3] L. Chayes, J. Machta, Graphical representations and cluster algorithms. Part I: Discrete spin system, Phys. A239 (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. Zbl0968.60092MR1742888
- [6] R. Diestel, Graph Theory, Springer-Verlag, Berlin, 1997. Zbl0859.05001MR1448665
- [7] P. Diaconis, D. Stroock, Geometric bounds for eigenvalues of Markov chains, Ann. Appl. Probab.1 (1) (1991) 36-61. Zbl0731.60061MR1097463
- [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. Zbl0184.40403
- [9] S. Edwards, P. Anderson, Theory of spin glasses, J. Phys. F5 (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. Zbl0726.60069MR1097464
- [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. Zbl0935.60084MR1627811
- [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. Zbl0978.82098MR1796026
- [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. Zbl0851.60096MR1382221
- [15] R.J. Glauber, Time dependent statistics of the Ising model, J. Math. Phys.4 (1963) 294-307. Zbl0145.24003MR148410
- [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. Zbl0522.60097MR692943
- [18] O. Lanford, D. Ruelle, Observables at infinity and states with short range correlations in statistical mechanics, Comm. Math. Phys.13 (1969) 194-215. MR256687
- [19] T. Liggett, Interacting Particle Systems, Springer-Verlag, Berlin, 1985. Zbl0559.60078MR776231
- [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. Zbl0779.60078MR1233852
- [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. Zbl0793.60110MR1269387
- [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. Zbl0793.60111MR1269388
- [23] F. Martinelli, E. Olivieri, R.H. Schonmann, Systems weak mixing implies strong mixing, Comm. Math. Phys.165 (1) (1994) 33-47. Zbl0811.60097MR1298940
- [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. Zbl0739.60098
- [25] C.M. Newman, D.L. Stein, Zero-temperature dynamics of Ising spin systems following a deep quench: results and open problems, Phys. A279 (2000) 159-168. MR1797138
- [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. Zbl0679.60102MR1027910
- [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. Zbl0758.60070MR1182416
- [29] B. Zegarlinski, On log-Sobolev inequalities for infinite lattice systems, Lett. Math. Phys.20 (3) (1990) 173-182. Zbl0717.47015MR1074698
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