THE LOW-TEMPERATURE PHASE OF KAC-ISING MODELS

We analyze the low-temperature phase of ferromagnetic Kax-Ising models in dimensions d greater than or equal to 2. We show that if the range of interactions is gamma(-1), then two disjoint translation-invariant Gibbs states exist if the inverse temperature beta satisfies beta - 1 greater than or equal to gamma(kappa), where kappa = d(1 - epsilon)/( 2d + 2)(d + 1), for any epsilon > 0. The proof involves the blocking p rocedure usual for Kac models and also a contour representation for th e resulting long-range (almost) continuous-spin system which is suitab le for the use of a variant of the Peierls argument.