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 a strictly positive critical value such that for p less than this threshold 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, Andrea; Causin, Andrea; Piatnitski, Andrey; Solci, Margherita. - 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

Andrea Causin;Margherita Solci
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 a strictly positive critical value such that for p less than this threshold 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.
2018
Asymptotic behaviour of ground states for mixtures of ferromagnetic and antiferromagnetic interactions in a dilute regime / Braides, Andrea; Causin, Andrea; Piatnitski, Andrey; Solci, Margherita. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - 171:6(2018), pp. 1096-1111. [10.1007/s10955-018-2051-8]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11388/209247
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