We study a system of N layers with a Kac horizontal interaction of parameter γ > 0 and a Kac vertical interaction of parameter γ 1/2. 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.
A model for interfaces and its mesoscopic limit / Aleandri, M.; Di Giulio, V.. - In: MATHEMATICS AND MECHANICS OF COMPLEX SYSTEMS. - ISSN 2326-7186. - 6:4(2018), pp. 267-291. [10.2140/memocs.2018.6.267]
A model for interfaces and its mesoscopic limit
Aleandri M.
;
2018
Abstract
We study a system of N layers with a Kac horizontal interaction of parameter γ > 0 and a Kac vertical interaction of parameter γ 1/2. 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.| File | Dimensione | Formato | |
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