Poisson approximation for large contours in low-temperature Ising models

We consider the contour representation of the infinite volume Ising model at any fixed inverse temperature beta > beta*, the solution of Sigma(theta:theta contains0)e(-beta\theta\) = 1. Let mu be the infinite-volume "+" measure. Fix V subset of Z(d), lambda > 0 and a (large) N such that calling G(N,V). the set of contours of length at least N intersecting V, there are in average lambda contours in G(N,V) under mu. We show that the total Variation distance between the law of (gamma: gamma is an element of G(N,V)) under mu and a Poisson process is bounded by a constant depending on beta and lambda times e(-(beta-beta*)N). The proof builds on the Chen-Stein method as presented by Arratia, Goldstein and Gordon. The control of the correlations is obtained through the loss-network space-time representation of contours due to Fernandez, Ferrari and Garcia, (C) 2000 Published by Elsevier Science B.V. All rights reserved.