The simplest spin glass

We study a system of Ising spins with quenched random infinite ranged p-spin interactions. For p → ∞, we can solve this model exactly either by a direct microcanonical argument, or through the introduction of replicas and Parisi's ultrametric ansatz for replica symmetry breaking, or by means of...

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Bibliographic Details
Published inNuclear physics. B Vol. 240; no. 4; pp. 431 - 452
Main Authors Gross, D.J., Mezard, M.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.01.1984
Elsevier
Subjects
Exact sciences and technology
Nonlinear dynamics and nonlinear dynamical systems
Physics
Statistical physics, thermodynamics, and nonlinear dynamical systems
Spin glass
Ising model
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Summary:We study a system of Ising spins with quenched random infinite ranged p-spin interactions. For p → ∞, we can solve this model exactly either by a direct microcanonical argument, or through the introduction of replicas and Parisi's ultrametric ansatz for replica symmetry breaking, or by means of TAP mean field equations. Although the model is extremely simple it retains the characteristic features of a spin glass. We use it to confirm the methods that have been applied in more complicated situations and to explicitlu exhibit the structure of the spin glass phase.
ISSN:0550-3213
1873-1562
DOI:10.1016/0550-3213(84)90237-2