Relaxation to equilibrium for two dimensional disordered Ising systems in the Griffiths phase *

Communications in Mathematical Physics

Volumn 189, Issue 2, 1997, Pages 323-335

  Cesi, F ^a   Maes, C ^b   Martinelli, F ^c  

^a UNIVERSITÀ DI ROMA LA SAPIENZA   (Italy)

^b UNIVERSITY OF LEUVEN   (Belgium)

^c NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040454786     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050205     Document Type: Article

References (30)

1. Palmer, R.G., Stein, D.L., Abrahams, E. and Anderson, P.W.: Models of hierarchically constrained dynamics for glassy relaxation. Phys. Rev. Lett. 53, No 10, 958 (1984)
2. Aizenman, M., Barsky, D.J. and Fernandez, R.: The phase transition in a general class of Ising-type models is sharp. J. Stat. Phys. 47, No. 3/4, 343 (1987)
3. Aizenman, M., Chayes, J.T., Chayes, L. and Newman, CM: The phase boundary in dilute and random Ising and Potts ferromagnets. J.Phys.A: Math. Gen. 20, L313 (1987)
4. Bassalygo, L.A. and Dobrushin, R.L.: Uniqueness of a Gibbs field with random potential- an elementary approach. Theory Prob. Appl. 31, No 4, 572 (1986)
5. Bray, A.J.: Upper and lower bounds on dynamic correlations in the Griffiths phase. J.Phys.A: Math. Gen. 22, L81 (1989)
6. c. Phys. Rev. Lett. 60, No 8 720 (1988)
7. van den Berg, J.: A constructive mixing condition for 2-D Gibbs measures with random interactions. Preprint 1996
8. Cesi, F., Guadagni, G., Martinelli, F. and Schonmann, R.H.: On the 2D stochastic Ising model in the phase coexistence region close to the critical point. J. Stat. Phys. 85, No 1/2, 55 (1996)
9. Cesi, F., Maes, C. and Martinelli, F.: Relaxation of disordered magnets in the Griffiths phase. Roma preprint 1996, Commun. Math. Phys., in press
10. De Dominicis, C., Orland, H. and Lainée, F.: Stretched exponential in systems with random free energies. J.Physique Lett. 46, L-463 (1985)
11. Dhar, D., Randeria, M. and Sethna, J.P. Griffiths singularities in the dynamics of disordered Ising models. Europhys. Lett., 5, No 6, 485, (1988)
12. Von Dreyfus, H., Klein, A. and Perez, J.F.: Taming Griffiths singularities: infinite differentiability of quenched correlations functions. Commun. Math. Phys. 170, 21 (1995)
13. Fröhlich, J.: Mathematical aspects of the physics of disordered systems. In Critical Phenomena, Random Systems, Gauge Theories. Eds. K.Osterwalder and R. Stora, Amsterdam: Elsevier, 1986
14. Gielis, G. and Maes, C.: Percolation techniques in disordered spin flip dynamics: Relaxation to the unique invariant measure. Commun.Math.Phys. 177, 83 (1995)
15. Gielis, G. and Maes, C.: Local analyticity and bounds on the truncated correlation functions in disordered systems. Markov Processes Relat. Fields 1, 459 (1995)
16. Gielis, G. and Maes, C.: The uniqueness regime of Gibbs fields with unbounded disorder. J. Stat. Phys. 81, No. 3/4, 829 (1995)
17. Griffiths, R.: Non-analytic behaviour above the critical point in a random Ising ferromagnet. Phys. Rev. Lett. 23, 17 (1969)
18. Grimmett, G.: Percolation. Berlin-Heidelberg-New York: Springer-Verlag, 1989
19. Guionnet, A. and Zegarlinski, : Decay to equilibrium in random spin systems on a lattice. Commun. Math.Phys. 181, 703 (1996)
20. Guionnet, A. and Zegarlinski, B.: Decay to equilibrium in random spin systems on a lattice II. J. Stat. Phys. 86, 899 (1997)
21. Jain, S.: Anomalously slow relaxation in the diluted Ising model below the percolation threshold. Physica A 218, 279 (1995)
22. Higuchi, Y.: Coexistence of infinite (*)-clusters II: - Ising percolation in two dimension. Prob. Th. Rel. Fields 97, 1 (1993)
23. Liggett, T.M.: Interacting particles systems. Berlin-Heidelberg-New York: Springer-Verlag, 1985
24. Martinelli, F: On the two dimensional dynamical Ising model in the phase coexistence region. J. Stat. Phys. 76, No. 5/6 1179 (1994)
25. Martinelli, F. and Olivieri, E.: Approach to equilibrium of Glauber dynamics in the one phase region I: The attractive case. Commun. Math. Phys. 161, 447 (1994)
26. Martinelli, F., Olivieri, E. and Schonmann, R.H.: For Gibbs state of 2D lattice spin systems weak mixing implies strong mixing. Commun. Math. Phys. 165, 33 (1994)
27. Newman, C.M.: Disordered Ising systems and random cluster representation. In: Probability and Phase Transition edited by G.Grimmet, NATO ASI Series Vol. 120 (1993)
28. Ogielski, A.T.: Dynamics of three dimensional Ising spin glasses in thermal equilibrium. Phys. Rev. B, 32, No 11, 7384 (1985)
29. Olivieri, E., Perez, F. and Goulart, S.-Rosa-Jr.: Some rigorous results on the phase diagram of the dilute Ising model. Phys. Lett. 94A, No 6,7, 309 (1983)
30. Randeria, M., Sethna, J.P. and Palmer, R.G.: Low-frequency relaxation in Ising spin-glasses. Phys. Rev. Lett. 54, No. 12, 1321 (1985)