Abstract

We study a system of $N$ layers with a Kac horizontal interaction of parameter $\gamma >0$ and a Kac vertical interaction of parameter ${\gamma }^{1∕2}$. We shall prove that the limit free energy functional is the rate function of the large deviations of the Gibbs measure (of a canonical constrained magnetization). The limit free energy functional is achieved as a $\Gamma$-limit for $\gamma \to 0$ for magnetizations with fixed average. Among all such magnetizations there exists a quasiconstant magnetization that minimizes the energy.

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