2018/08/07 by Liming Pan, Simone Franchini, Pan, Liming +1
Materials Science · Mathematics · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Material Dynamics and Properties #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1808.02542
openalex publication_date 2018/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.