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

Permanent link
https://hdl.handle.net/10037/14989
DOI
https://doi.org/10.1007/s10955-018-2051-8
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accepted manuscript (PDF)
Date
2018-04-30
Type
Journal article
Peer reviewed

Author
Braides, Andrea; Causin, Andrea; Piatnitski, Andrey; Solci, Margherita
Abstract
We consider randomly distributed mixtures of bonds of ferromagnetic and antiferromagnetic type in a two-dimensional square lattice with probability 1−p 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 Z 2 Z2 . We prove that there exists p 0 p0 such that for p≤ p 0 p≤p0 such minimizers are characterized by a majority phase; i.e., they take identically the value 1 or −1 −1 except for small disconnected sets. A deterministic analogue is also proved.
Description
Accepted manuscript version, 12 months embargo. Published version at: https://doi.org/10.1007/s10955-018-2051-8
Publisher
Springer Nature
Citation
Braides A., Causin,A., Piatnitski, A, Solci, M.(2018) Asymptotic Behaviour of Ground States for Mixtures of Ferromagnetic and Antiferromagnetic Interactions in a Dilute Regime. Journal of statistical physics,171(6),1096-1111. https://doi.org/10.1007/s10955-018-2051-8
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