Exact results on spin glass models

Hidetoshi Nishimori

Research output: Contribution to journalConference article

6 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)68-75
Number of pages8
JournalPhysica A: Statistical Mechanics and its Applications
Volume306
DOIs
Publication statusPublished - 2002 Apr 1
Externally publishedYes
Event21th IUPAP Conference on Invited Papares (STATPHYS 21) - Cancun, Mexico
Duration: 2001 Jul 152001 Jul 21

Keywords

  • Gauge theory
  • Ising model
  • Random-phase XY model
  • Spin glass
  • Spin wave theory
  • Villain model

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

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