 94175 Pirmin Lemberger.
 Large field versus small field expansions and Sobolev inequalities
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Jun 2, 94

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Abstract. We study a model for a two dimensional random interface $\phi(x)$,
\mbox{$x\in\R^2$} described by a
massless gaussian measure perturbed by a weak potential \linebreak
\mbox{$V(\phi)=\frac{\eps^2}{2}(\ex {\alpha\phi}1)^2$}.
Such a model occurs for instance in a phenomenological
description of the wetting transition. We prove that, provided $\alpha$ is
small enough, the twopoint function decreases exponentially with a rate of
order $m\equiv\eps\alpha$ which is just the mean field value.
The large field region problem due to the fact that $V(\phi)$ remains bounded
when $\phi\rightarrow +\infty$ is treated by means of a large field versus
small field expansion combined with elementary Sobolev inequalities. The
paper is intended to be accessible to nonexperts.
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