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 p0 such that for p≤ p0 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.
Asymptotic Behaviour of Ground States for Mixtures of Ferromagnetic and Antiferromagnetic Interactions in a Dilute Regime / Braides, A.; Causin, A.; Piatnitski, A.; Solci, M.. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - 171:6(2018), pp. 1096-1111. [10.1007/s10955-018-2051-8]
Asymptotic Behaviour of Ground States for Mixtures of Ferromagnetic and Antiferromagnetic Interactions in a Dilute Regime
Braides A.;
2018-01-01
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 Z2. We prove that there exists p0 such that for p≤ p0 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
