98-713 Francois DUNLOP, Jacques MAGNEN

A Wulff Shape from Constructive Field Theory (484K, postscript) Nov 13, 98

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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.

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