  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.
