The marginally stable Bethe lattice spin glass revisited

TL;DR

This paper develops a non-perturbative cavity method approach to analyze the marginal stability of Bethe lattice spin glasses, addressing limitations of previous approximations and providing insights into their equilibrium behavior.

Contribution

It introduces a novel non-perturbative cavity method framework to study marginal stability in Bethe lattice spin glasses, overcoming previous technical and approximation limitations.

Findings

Proposes a consistent non-perturbative approach

Addresses the marginal stability in spin glasses

Provides a more accurate theoretical framework

Abstract

Bethe lattice spins glasses are supposed to be marginally stable, i.e. their equilibrium probability distribution changes discontinuously when we add an external perturbation. So far the problem of a spin glass on a Bethe lattice has been studied only using an approximation where marginally stability is not present, which is wrong in the spin glass phase. Because of some technical difficulties, attempts at deriving a marginally stable solution have been confined to some perturbative regimes, high connectivity lattices or temperature close to the critical temperature. Using the cavity method, we propose a general non-perturbative approach to the Bethe lattice spin glass problem using approximations that should be hopeful consistent with marginal stability.