High temperature Sherrington-Kirkpatrick model for general spins

Philippe Carmona

High temperature Sherrington-Kirkpatrick model for general spins

概率论 2007-05-23 v1

作者: Philippe Carmona

摘要

Francesco Guerra and Fabio Toninelli have developped a very powerful technique to study the high temperature behaviour of the Sherrington-Kirkpatrick mean field spin glass model. They show that this model is asymptoticaly comparable to a linear model. The key ingredient is a clever interpolation technique between the two different Hamiltonians describing the models. This paper contribution to the subject are the following: (1) The replica-symmetric solution holds for general spins, not just $\pm 1$ valued. (2) The proof does not involve cavitation but only first order differential calculus and Gaussian integration by parts.

关键词

spin glasses

引用

@article{arxiv.math/0210140,
  title  = {High temperature Sherrington-Kirkpatrick model for general spins},
  author = {Philippe Carmona},
  journal= {arXiv preprint arXiv:math/0210140},
  year   = {2007}
}

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