The low-temperature phase of Kac-Ising models

Abstract

We analyse the low temperature phase of ferromagnetic Kac-Ising models in dimensions $d\ge 2$. We show that if the range of interactions is $\g^{-1}$, then two disjoint translation invariant Gibbs states exist, if the inverse temperature $\b$ satisfies $\b -1\geq \g^\k$ where $\k=\frac {d(1-\e)}{(2d+1)(d+1)}$, for any $\e>0$. The prove involves the blocking procedure usual for Kac models and also a contour representation for the resulting long-range (almost) continuous spin system which is suitable for the use of a variant of the Peierls argument.

19pp, Plain TeX

References in corpus (1)

• Distribution of overlap profiles in the one-dimensional Kac-Hopfield model

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