On the connection between spin glasses and gauge field theories

A simple connection between Ising spin glasses and the Z 2 lattice gauge theory, at negative plaquette temperatures, is presented. It is first shown that annealed models give useful lower bounds on the free energy and ground-state energy of spin glasses. However, they have unphysical low temperature...

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Bibliographic Details
Published in:Physics reports 1980-01, Vol.67 (1), p.47-54
Main Authors: Toulouse, G., Vannimenus, J.
Format: Article
Language:English
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Summary:A simple connection between Ising spin glasses and the Z 2 lattice gauge theory, at negative plaquette temperatures, is presented. It is first shown that annealed models give useful lower bounds on the free energy and ground-state energy of spin glasses. However, they have unphysical low temperature properties (e.g. a negative entropy), which are related to a temperature dependence of the frustration. A restricted annealing scheme is presented which remedies this deficiency through the introduction of a pure gauge coupling counterterm. The possible phase diagrams of the lattice gauge system and their relevance to spin glass transitions are discussed.
ISSN:0370-1573
1873-6270
DOI:10.1016/0370-1573(80)90078-2