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Occurrence, Repetition and Matching of Patterns in the Low-temperature Ising Model

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Abstract

We continue our study of the exponential law for occurrences and returns of patterns in the context of Gibbsian random fields. For the low-temperature plus-phase of the Ising model, we prove exponential laws with error bounds for occurrence, return, waiting and matching times. Moreover we obtain a Poisson law for the number of occurrences of large cylindrical events and a Gumbel law for the maximal overlap between two independent copies. As a by-product, we derive precise fluctuation results for the logarithm of waiting and return times. The main technical tool we use, in order to control mixing, is disagreement percolation

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Authors and Affiliations

  1. CPhT CNRS-Ecole Polytechnique, 91128, Palaiseau Cedex, France

    J. -R. Chazottes

  2. Faculteit Wiskunde en Informatica, Technische Universiteit Eindhoven, Postbus 513, 5600, MB Eindhoven, The Netherlands

    F. Redig

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  1. J. -R. Chazottes
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  2. F. Redig
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Correspondence to J. -R. Chazottes.

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Chazottes, J.R., Redig, F. Occurrence, Repetition and Matching of Patterns in the Low-temperature Ising Model. J Stat Phys 121, 579–605 (2005). https://doi.org/10.1007/s10955-005-7575-z

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  • DOI: https://doi.org/10.1007/s10955-005-7575-z

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