The Parisi formula for mixed $p$-spin models
Probability
2014-04-01 v2
Abstract
The Parisi formula for the free energy in the Sherrington-Kirkpatrick and mixed -spin models for even was proved in the seminal work of Michel Talagrand [Ann. of Math. (2) 163 (2006) 221-263]. In this paper we prove the Parisi formula for general mixed -spin models which also include -spin interactions for odd . Most of the ideas used in the paper are well known and can now be combined following a recent proof of the Parisi ultrametricity conjecture in [Ann. of Math. (2) 177 (2013) 383-393].
Keywords
Cite
@article{arxiv.1112.4409,
title = {The Parisi formula for mixed $p$-spin models},
author = {Dmitry Panchenko},
journal= {arXiv preprint arXiv:1112.4409},
year = {2014}
}
Comments
Published in at http://dx.doi.org/10.1214/12-AOP800 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)