Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/52700
Type: Artigo de periódico
Title: Loss network representation of Peierls countours
Author: Fernandez, R
Ferrari, PA
Garcia, NL
Abstract: We present a probabilistic approach for the study of systems with exclusions in the regime traditionally studied via cluster-expansion methods. In this paper we focus on its application for the gases of Peierls contours found in the study of the Ising model at low temperatures, but most of the results are general. We realize the equilibrium measure as the invariant measure of a loss network process whose existence is ensured by a subcriticality condition of a dominant branching process. In this regime the approach yields, besides existence and uniqueness of the measure, properties such as exponential space convergence and mixing, and a central limit theorem. The loss network converges exponentially fast to the equilibrium measure, without metastable traps, This convergence is faster at low temperatures, where it leads to the proof of an asymptotic Poisson distribution of contours. Our results on the mixing properties of the measure are comparable to those obtained with "duplicated-variables expansion," used to treat systems with disorder and coupled map lattices. It works in a larger region of validity than usual cluster-expansion formalisms, and it is not tied to the analyticity of the pressure. In fact, it does not lead to any kind of expansion for the latter, and the properties of the equilibrium measure are obtained without resorting to combinatorial or complex analysis techniques.
Subject: Peierls contours
animal models
loss networks
Ising model
oriented percolation
central limit theorem
Poisson approximation
Country: EUA
Editor: Inst Mathematical Statistics
Rights: aberto
Date Issue: 2001
Appears in Collections:Artigos e Materiais de Revistas Científicas - Unicamp

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