English

Exact results on spin glass models

Disordered Systems and Neural Networks 2009-11-07 v1 Statistical Mechanics

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

Cite

@article{arxiv.cond-mat/0201056,
  title  = {Exact results on spin glass models},
  author = {Hidetoshi Nishimori},
  journal= {arXiv preprint arXiv:cond-mat/0201056},
  year   = {2009}
}

Comments

9 pages, Proceedings of STATPHYS21, to be published in Physica A

R2 v1 2026-07-22T10:32:46.571Z