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 [8], where the strict convexity of potential was crucial in their proof.
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Acknowledgement
Codina Cotar thanks David Brydges and Haru Pinson for invaluable advice and suggestions during the writing of the manuscript.
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Communicated by H. Spohn
Supported by the DFG-Forschergruppe 718 ‘Analysis and stochastics in complex physical systems’.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Cotar, C., Deuschel, JD. & Müller, S. Strict Convexity of the Free Energy for a Class of Non-Convex Gradient Models. Commun. Math. Phys. 286, 359–376 (2009). https://doi.org/10.1007/s00220-008-0659-2
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DOI: https://doi.org/10.1007/s00220-008-0659-2