English

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 pp-spin models for even p2p\geq2 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 pp-spin models which also include pp-spin interactions for odd pp. 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)

R2 v1 2026-06-21T19:53:52.983Z