 98474 Fern\'andez, R., Ferrari, P., Garcia, N. L.
 Loss network representation of Peierls contours
(86K, LaTeX)
Jun 23, 98

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. We present a probabilistic approach for the study of systems with exclusions,
in the regime traditionally studied via clusterexpansion 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
lossnetwork 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
``duplicatedvariables expansion'', used to treat systems with disorder and
coupled map lattices. It works in a larger region of validity than usual
clusterexpansion 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.
 Files:
98474.tex