01-65 Rapha\"el Cerf, Richard Kenyon

The low-temperature expansion of the Wulff crystal in the $3$D Ising model (360K, Postscript) Feb 7, 01

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Abstract. We compute the expansion of the surface tension of the 3D random cluster model for $q\geq 1$ in the limit where $p$ goes to~$1$. We also compute the asymptotic shape of a plane partition of $n$ as $n$ goes to $\infty$. This same shape determines the asymptotic Wulff crystal in the $3$D Ising model (and more generally in the $3$D random cluster model for $q\geq 1$) as the temperature goes to $0$.

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