Translator Disclaimer
May 2002 Clusters and recurrence in the two-dimensional zero-temperature stochastic ising model
Federico Camia, Emilio De Santis, Charles M. Newman
Ann. Appl. Probab. 12(2): 565-580 (May 2002). DOI: 10.1214/aoap/1026915616

Abstract

We analyze clustering and (local) recurrence of a standard Markov process model of spatial domain coarsening. The continuous time process, whose state space consists of assignments of $+1$ or $-1$ to each site in $\mathbf{Z}^2$, is the zero-temperature limit of the stochastic homogeneous Ising ferromagnet (with Glauber dynamics): the initial state is chosen uniformly at random and then each site, at rate 1, polls its four neighbors and makes sure it agrees with the majority, or tosses a fair coin in case of a tie. Among the main results (almost sure, with respect to both the process and initial state) are: clusters (maximal domains of constant sign) are finite for times $t< \infty$, but the cluster of a fixed site diverges (in diameter) as $t \to \infty$; each of the two constant states is (positive) recurrent. We also present other results and conjectures concerning positive and null recurrence and the role of absorbing states.

Citation

Download Citation

Federico Camia. Emilio De Santis. Charles M. Newman. "Clusters and recurrence in the two-dimensional zero-temperature stochastic ising model." Ann. Appl. Probab. 12 (2) 565 - 580, May 2002. https://doi.org/10.1214/aoap/1026915616

Information

Published: May 2002
First available in Project Euclid: 17 July 2002

zbMATH: 1020.60094
MathSciNet: MR1910640
Digital Object Identifier: 10.1214/aoap/1026915616

Subjects:
Primary: 60J25, 60K35
Secondary: 82C20, 82C22

Rights: Copyright © 2002 Institute of Mathematical Statistics

JOURNAL ARTICLE
16 PAGES


SHARE
Vol.12 • No. 2 • May 2002
Back to Top