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

created by braidesa on 16 Jan 2017
modified on 24 Apr 2018

[BibTeX]

Accepted Paper

Inserted: 16 jan 2017
Last Updated: 24 apr 2018

Journal: J. Stat. Phys.
Year: 2018
Doi: 10.1007/s10955-018-2051-8

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.