SURFACE-TENSION IN ISING SYSTEMS WITH KAC POTENTIALS

We consider an Ising spin system with Kac potentials in a torus of Z(d ), d greater than or equal to 2, and fix the temperature below its Leb owitz-Penrose critical value. We prove that when the Kac scaling param eter gamma vanishes, the log of the probability of an interface become s proportional to its area and the surface tension, related to the pro portionality constant, converges to the van der Waals surface tension. The results are based on the analysis of the rate functionals for Gib bsian large deviations and on the proof that they Gamma-converge to th e perimeter functional of geometric measure theory (which extends the notion of area). Our considerations include nonsmooth interfaces, prov ing that the Gibbsian probability of an interface depends only on its area and not on its regularity.