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Chaotic time dependence in a disordered spin system
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  • Published: October 1999

Chaotic time dependence in a disordered spin system

  • L. R. G. Fontes1,
  • M. Isopi2 &
  • C. M. Newman3 

Probability Theory and Related Fields volume 115, pages 417–443 (1999)Cite this article

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  • 14 Citations

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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.

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Authors and Affiliations

  1. Instituto de Matemática e Estatística, Universidade de São Paulo, Cx.Postal 66281, 05315-970 São Paulo, SP, Brasil. e-mail: lrenato@ime.usp.br, , , , , , BR

    L. R. G. Fontes

  2. Dipartimento di Matematica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 2, I-00185 Roma, Italia. e-mail: isopi@mat.uniroma1.it, , , , , , IT

    M. Isopi

  3. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA. e-mail: newman@cims.nyu.edu, , , , , , US

    C. M. Newman

Authors
  1. L. R. G. Fontes
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  2. M. Isopi
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  3. C. M. Newman
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Received: 10 August 1998

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Fontes, L., Isopi, M. & Newman, C. Chaotic time dependence in a disordered spin system. Probab Theory Relat Fields 115, 417–443 (1999). https://doi.org/10.1007/s004400050244

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  • Issue Date: October 1999

  • DOI: https://doi.org/10.1007/s004400050244

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  • Mathematics Subject Classification (1991): 60K35, 82B44
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