Free energy of bipartite Sherrington-Kirkpatrick model
Abstract
In this paper we study the bipartite version of Sherrington-Kirkpatrick model. We prove that the free energy density is given by an analogue of the Parisi formula, that contains both the usual overlap and an additional new type of overlap. Following Panchenko, we prove the upper bound of the formula by Guerra's replica symmetry breaking interpolation, then the matching lower bound by Ghirlanda-Guerra identities and the Aizenman-Sims-Starr scheme. Based on this result we study the stability of the replica symmetric solution. A new phase exhibiting partial replica symmetry breaking is observed, where the broken phase is realized in the larger group only.
Keywords
Cite
@article{arxiv.1808.02542,
title = {Free energy of bipartite Sherrington-Kirkpatrick model},
author = {Liming Pan and Simone Franchini},
journal= {arXiv preprint arXiv:1808.02542},
year = {2018}
}
Comments
We retired the paper after finding a major technical issue. In particular, the proposed partially RSB-broken scenario only represent a lower bound for the free energy and not a tight approximation