Strict convexity of the free energy for non-convex gradient models at moderate β

Codina Cotar, Jean-Dominique Deuschel, and Stefan Müller

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Submission date: 09. Jan. 2008
Pages: 19
published in: Communications in mathematical physics, 286 (2009) 1, p. 359-376 
DOI number (of the published article): 10.1007/s00220-008-0659-2
Bibtex
with the following different title: Strict convexity of the free energy for a class of non-convex gradient models
MSC-Numbers: 60K35, 82B24, 35J15
Keywords and phrases: effective non-convex gradient interface models, surface tension, strict convexity, Helffer-Sjöstrand representation
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Abstract:
We consider a gradient interface model on the lattice with interaction potential which is a non-convex perturbation of a convex potential. We show using a one-step multiple scale analysis the strict convexity of the surface tension at high temperature. This is an extension of Funaki and Spohn's result [10], where the strict convexity of potential was crucial in their proof.