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Dynamics of a cluster model of spin glasses

Authors
Journal
Physica B+C
0378-4363
Publisher
Elsevier
Publication Date
Volume
106
Issue
1
Identifiers
DOI: 10.1016/0378-4363(81)90013-9
Disciplines
  • Physics

Abstract

Abstract We consider a model of a random magnetic system, represented by Ising spins, and defined by a Hamiltonian consisting of an intercluster and intracluster parts. Assuming that all the clusters are of identical size and shape, we approximate the intracluster Hamiltonian by a “self-interaction” term of the type KΣ ν S 2 ν, where K is a given positive parameter and S ν is the total (Ising) spin of the cluster. The intercluster part of the Hamiltonian is taken to be Σ μΣ ν J μν S μ S ν, where the intercluster coupling J μν is assumed to be a random variable with a Gaussian distribution. Starting with a master equation for such a system and working in the mean-field and linearized version, we obtain the magnetization, dynamic susceptibility and spin correlation function. An important qualitative feature of the ferromagnetic cluster formation is that dynamical quantities like magnetization and spin correlation functions decay at a slower rate than when the clusters are absent.

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