THE FREE ENERGY IN A MULTI-SPECIES SHERRINGTON-KIRKPATRICK MODEL
成果类型：
Article
署名作者：
Panchenko, Dmitry
署名单位：
University of Toronto
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/14-AOP967
发表日期：
2015
页码：
3494-3513
关键词：
摘要：
The authors of [Ann. Henri Poincare 16 (2015) 691-708] introduced a multi-species version of the Sherrington-Kirkpatrick model and suggested the analogue of the Parisi formula for the free energy. Using a variant of Guerra's replica symmetry breaking interpolation, they showed that, under certain assumption on the interactions, the formula gives an upper bound on the limit of the free energy. In this paper we prove that the bound is sharp. This is achieved by developing a new multi-species form of the Ghirlanda-Guerra identities and showing that they force the overlaps within species to be completely determined by the overlaps of the whole system.