Exact results on spin glass models

Hidetoshi Nishimori

Physica A: Statistical Mechanics and its Applications, 2002, vol. 306, issue C, 68-75

Abstract: Exact and/or rigorous results are reviewed for the Ising and XY/Villain spin glasses in finite dimensions, such as the exact energy, correlation identities and a functional relation between the distribution functions of ferromagnetic and spin glass order parameters. This last relation is useful to prove that the phase space is not complex on a line in the phase diagram. The spin wave theory neglecting periodicity is shown to give exact results for the Villain model on a line in the phase diagram. Implications of this fact on the renormalization-group results for the random-phase XY/Villain model in two dimensions are discussed.

Keywords: Spin glass; Ising model; Random-phase XY model; Villain model; Spin wave theory; Gauge theory (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:306:y:2002:i:c:p:68-75

DOI: 10.1016/S0378-4371(02)00486-7

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