Title: Asymptotic behaviour of ground states for mixtures of ferromagnetic and antiferromagnetic interactions in a dilute regime,
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.