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.