Asymptotic Behaviour of Ground States for Mixtures of Ferromagnetic and Antiferromagnetic Interactions in a Dilute Regime

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 Z2. We prove that there exists p0such that for p≤ p0such 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.