Clusters and recurrence in the two-dimensional zero-temperature stochastic Ising model

Annals of Applied Probability

Volumn 12, Issue 2, 2002, Pages 565-580

  Camia, Federico ^a   De Santis, Emilio ^b   Newman, Charles M ^c  

^a POLYTECHNIC UNIVERSITY   (United States)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

^c NEW YORK UNIVERSITY   (United States)

Author keywords

Clusters; Coarsening; Percolation; Recurrence; Stochastic Ising model; Transience; Zero temperature

Indexed keywords

EID: 0036339031     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1026915616     Document Type: Article

References (21)

1. d. Ann. Probab. 11 706-713.
2. BRAY, A. J. (1994). Theory of phase-ordering kinetics. Adv. Phys. 43 357-459.
3. COX, J. T. and GRIFFEATH, D. (1986). Diffusive clustering in the two-dimensional voter model. Ann. Probab. 14 347-370.
4. COX, J. T. and KLENKE, A. (2000). Recurrence and ergodicity of interacting particle systems. Probab. Theory Related Fields 116 239-255.
5. DERRIDA, B. (1995). Exponents appearing in the zero-temperature dynamics of the 1D Potts model. J. Phys. A 28 1481-1491.
6. DERRIDA, B., HAKIM, V. and PASQUIER, V. (1995). Exact first-passage exponents of 1D domain growth: Relation to a reaction-diffusion model. Phys. Rev. Lett. 75 751-754.
7. DURRETT, R. (1988). Lecture Notes on Particle Systems and Percolation. Wadsworth and Brooks/Cole, Advanced Books and Software, Pacific Grove, CA.
8. FONTES, L. R., ISOPI, M. and NEWMAN, C. M. (1999). Chaotic time dependence in a disordered spin system. Probab. Theory Related Fields 115 417-443.
9. FONTES, L. R., ISOPI, M. and NEWMAN, C. M. (2000). Random walks with strongly inhomogeneous rates and singular diffusion: Convergence, localization and aging in one dimension. Ann. Probab. 30 579-604.
10. FONTES, L. R., SIDORAVICIUS, V. and SCHONMANN, R. H. (2001). Stretched exponential fixation in stochastic Ising models at zero temperature. Preprint mp-arc 01-287.
11. GANDOLFI, A., KEANE, M. and RUSSO, L. (1988). On the uniqueness of the infinite occupied cluster in dependent two-dimensional site percolation. Ann. Probab. 16 1147-1157.
12. GANDOLFI, A., NEWMAN, C. M. and STEIN, D. L. (2000). Zero-temperature dynamics of ±J spin glasses and related models. Comm. Math. Phys. 214 373-387.
13. HARRIS, T. E. (1977). A correlation inequality for Markov processes in partially ordered state spaces. Ann. Probab. 5 451-454.
14. HOLLEY, R. A. and LIGGETT, T. M. (1975). Ergodic theorems for weakly interacting systems and the voter model. Ann. Probab. 3 643-663.
15. HOWARD, C. D. (2000). Zero-temperature Ising spin dynamics on the homogeneous tree of degree three. J. Appl. Probab. 37 736-747.
16. LIGGETT, T. M. (1985). Interacting Particle Systems. Springer, New York.
17. NANDA, S., NEWMAN, C. M. and STEIN, D. L. (2000). Dynamics of Ising spin systems at zero temperature. In On Dobrushin's Way (from Probability Theory to Statistical Mechanics) (R. Minlos, S. Shlosman and Y. Suhov, eds.) 183-194. Amer. Math. Soc., Providence.
18. NEWMAN, C. M. and STEIN, D. L. (1999). Blocking and persistence in zero-temperature dynamics of homogeneous and disordered Ising models. Phys. Rev. Lett. 82 3944-3947.
19. NEWMAN, C. M. and STEIN, D. L. (1999). Equilibrium pure states and nonequilibrium chaos. J. Statist. Phys. 94 709-722.
20. NEWMAN, C. M. and STEIN, D. L. (2000). Zero-temperature dynamics of Ising spin systems following a deep quench: results and open problems. Physica A 279 156-168.
21. STAUFFER, D. (1994). Ising spinodal decomposition at T = 0 in one to five dimensions. J. Phys. A 27 5029-5032.