 98521 Deuschel J.D., Velenik Y.
 NonGaussian Surface Pinned by a Weak Potential
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Jul 22, 98

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Abstract. We consider a model of a twodimensional interface of the SOS type, with
finiterange, even, strictly convex, twice continuously differentiable
interactions. We prove that, under an arbitrarily weak potential favouring
zeroheight, the surface has finite mean square heights. We consider the cases
of both square well and $\delta$ potentials. These results extend previous
results for the case of nearestneighbours Gaussian interactions in \cite{DMRR}
and \cite{BB}. We also obtain estimates on the tail of the height distribution
implying, for example, existence of exponential moments. In the case of the
$\delta$ potential, we prove a spectral gap estimate for linear functionals. We
finally prove exponential decay of the twopoint function (1) for strong
$\delta$pinning and the above interactions, and (2) for arbitrarily weak
$\delta$pinning, but with finiterange Gaussian interactions.
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