On spin distributions for generic p-spin models

TL;DR

This paper introduces a new formula for spin distributions in generic p-spin glass models, linking them to PDE solutions and confirming the multiscale TAP equations as predicted by earlier theories.

Contribution

It provides an alternative expression for spin distributions and demonstrates their connection to PDEs and the multiscale TAP equations in p-spin models.

Findings

New formula for spin distributions

Spin statistics as PDE solutions

Validation of multiscale TAP equations

Abstract

We provide an alternative formula for spin distributions of generic p-spin glass models. As a main application of this expression, we write spin statistics as solutions of partial differential equations and we show that the generic p-spin models satisfy multiscale Thouless-Anderson-Palmer equations as originally predicted in the work of Mezard-Virasoro.