Quenched complexity of the p-spin spherical spin-glass with external magnetic field

TL;DR

This paper analyzes the complexity of p-spin spherical spin-glass models with an external magnetic field, establishing a connection between quenched and static 1-RSB methods and confirming results through dynamical analysis.

Contribution

It provides a detailed computation of the quenched complexity in the presence of an external field and clarifies the relationship between different 1-RSB approaches.

Findings

Established a mapping between quenched and static 1-RSB parameters

Computed the complexity of TAP states in the model

Validated results with dynamical analysis

Abstract

We consider the p-spin spherical spin-glass model in the presence of an external magnetic field as a general example of a mean-field system where a one step replica symmetry breaking (1-RSB) occurs. In this context we compute the complexity of the Thouless-Anderson-Palmer states, performing a quenched computation. We find what is the general connection between this method and the standard static 1-RSB one, formulating a clear mapping between the parameters used in the two different calculations. We also perform a dynamical analysis of the model, by which we confirm the validity of our results.