Thouless-Anderson-Palmer equations for the Multi-species Sherrington-Kirkpatrick model

TL;DR

This paper proves the TAP equations for local magnetization in the multi-species SK model, extending understanding of spin glasses at high temperature without requiring positive semi-definiteness of the variance matrix.

Contribution

It establishes the TAP equations for the MSK model at high temperature without the positive semi-definite constraint on the variance profile.

Findings

TAP equations hold at high temperature for general MSK models

Concentration results are used to establish the equations

No positive semi-definite assumption needed on the variance matrix

Abstract

We prove the Thouless-Anderson-Palmer (TAP) equations for the local magnetization in the multi-species Sherrington-Kirkpatrick (MSK) spin glass model. One of the key ingredients is based on concentration results established in~\cite{arXiv:2012.13381}. The equations hold at high temperature for general MSK model without positive semi-definite assumption on the variance profile matrix $\mathbf{\Delta}^2$.