Exact results on spin glass models

Details Exact results on spin glass models Exact results on spin glass models

2002-01-05

arxiv.org/abs/cond-mat/0201056v1

Physica A 306, 68-75 (2002)

Physics

Condensed Matter

Disordered Systems and Neural Networks

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

Scientific paper

10.1016/S0378-4371(02)00486-7

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.

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