Francois DUNLOP, Jacques MAGNEN
 A Wulff Shape from Constructive Field Theory
(484K, postscript)

ABSTRACT.  We consider a sessile droplet as given by a height function $h(x)$, 
subject to a Hamiltonian of the form $|\na h|^2+\la P(\na h)$, 
where $P$ is a polynomial and $\la$ is small. 
The corresponding Gibbs measure is conditioned on the value of the 
droplet volume ${\rm V}=\int_\La dx\, h(x)\,$, where $\La\sub\Re^2$ is 
a bounded domain of the plane. The droplet shape, in a scaling limit 
${\rm V}\approx|\La|^{3/2}\rightarrow\infty$, is then a Wulff 
shape, with logarithmic fluctuations. The proof, outlined in these 
proceedings, is based on a phase space cluster expansion and 
renormalization of a varying slope chemical potential.