Loss network representation of Peierls countours

We present a probabilistic approach for the study of systems with exclusion s in the regime traditionally studied via cluster-expansion methods. In thi s 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 resul ts are general. We realize the equilibrium measure as the invariant measure of a loss network process whose existence is ensured by a subcriticality c ondition of a dominant branching process. In this regime the approach yield s, besides existence and uniqueness of the measure, properties such as expo nential space convergence and mixing, and a central limit theorem. The loss network converges exponentially fast to the equilibrium measure, without m etastable traps, This convergence is faster at low temperatures, where it l eads to the proof of an asymptotic Poisson distribution of contours. Our re sults on the mixing properties of the measure are comparable to those obtai ned with "duplicated-variables expansion," used to treat systems with disor der 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 o f 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.