Rapha\"el Cerf, Richard Kenyon
The low-temperature expansion of the
Wulff crystal in the $3$D Ising model
(360K, Postscript)
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 $0$.