94-175 Pirmin Lemberger.

Large field versus small field expansions and Sobolev inequalities (147K, LaTeX) 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 two-point 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 non-experts.

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