Calculus of Variations and Geometric Measure Theory
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A. Braides - A. Causin - A. Piatnitski - M. Solci

Asymptotic behaviour of ground states for mixtures of ferromagnetic and antiferromagnetic interactions in a dilute regime

created by braidesa on 16 Jan 2017

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Submitted Paper

Inserted: 16 jan 2017
Last Updated: 16 jan 2017

Year: 2017

Abstract:

We consider randomly distributed mixtures of bonds of ferromagnetic and antiferromagnetic type in a two-dimensional square lattice with probability $1-p$ and $p$, respectively, according to an i.i.d. random variable. We study minimizers of the corresponding nearest-neighbour spin energy on large domains in ${\mathbb Z}^2$. We prove that there exists $p_0$ such that for $p\le p_0$ such minimizers are characterized by a majority phase; i.e., they take identically the value $1$ or $-1$ except for small disconnected sets. A deterministic analogue is also proved.

Keywords: ground states, Ising models, random spin systems, asymptotic analysis of periodic media


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