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.