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