Vol. 6, No. 4, 2018

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ISSN: 2325-3444 (e-only)
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A model for interfaces and its mesoscopic limit

Michele Aleandri and Venanzio Di Giulio

Vol. 6 (2018), No. 4, 267–291
Abstract

We study a system of N layers with a Kac horizontal interaction of parameter γ > 0 and a Kac vertical interaction of parameter γ12. We shall prove that the limit free energy functional is the rate function of the large deviations of the Gibbs measure (of a canonical constrained magnetization). The limit free energy functional is achieved as a Γ-limit for γ 0 for magnetizations with fixed average. Among all such magnetizations there exists a quasiconstant magnetization that minimizes the energy.

Keywords
Kac potential, mesoscopic limit, $\Gamma$-convergence
Mathematical Subject Classification 2010
Primary: 82B24
Milestones
Received: 11 July 2017
Revised: 21 June 2018
Accepted: 24 July 2018
Published: 1 October 2018

Communicated by Raffaele Esposito
Authors
Michele Aleandri
Gran Sasso Science Institute
L’Aquila
Italy
Venanzio Di Giulio
Università degli Studi dell’Aquila
L’Aquila
Italy