Chaotic time dependence in a disordered spin system

• 成果类型: Article
• 署名作者: Fontes, LRG; Isopi, M; Newman, CM
• 署名单位: Universidade de Sao Paulo; Sapienza University Rome; New York University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s004400050244
• 发表日期: 1999
• 页码: 417-443
• 关键词: dimensional contact-processes; random environment; survival; MODEL

摘要

Stochastic Ising and voter models on Z(d) are natural examples of Markov processes with compact state spaces. When the initial state is chosen uniformly at random, can it happen that the distribution at time t has multiple (subsequence) limits as t --> infinity? Yes for the d = 1 Voter Model with Random Rates (VMRR)- which is the same as a d = 1 rate-disordered stochastic Ising model at zero temperature - if the disorder distribution is heavy-tailed. No (at least in a weak sense) for the VMRR when the tail is light or d greater than or equal to 2, These results are based on an analysis of the localization properties of Random Walks with Random Rates. Mathematics Subject Classification (1991): 60K35, 82B44.