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Chaotic time dependence in a disordered spin system |
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| Authors: | L R G Fontes M Isopi C M Newman |
| Institution: | Instituto de Matemática e Estatística, Universidade de S?o Paulo, Cx.Postal 66281, 05315-970 S?o Paulo, SP, Brasil. e-mail: lrenato@ime.usp.br, BR Dipartimento di Matematica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 2, I-00185 Roma, Italia. e-mail: isopi@mat.uniroma1.it, IT Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA. e-mail: newman@cims.nyu.edu, US |
| Abstract: | 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→∞? 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≥ 2. These results are based on an analysis of the “localization” properties of Random Walks with Random Rates. Received: 10 August 1998 |
| Keywords: | Mathematics Subject Classification (1991): 60K35 82B44 |
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