About the Almeida-Thouless transition line in the Sherrington-Kirkpatrick mean field spin glass mode

TL;DR

This paper proves that in the Sherrington-Kirkpatrick spin glass model, the true free energy exceeds the replica symmetric approximation below the Almeida-Thouless line, confirming the onset of replica symmetry breaking.

Contribution

It rigorously establishes the strict inequality between the true free energy and the replica symmetric approximation below the Almeida-Thouless line.

Findings

True free energy exceeds replica symmetric approximation below the AT line

Confirms the presence of replica symmetry breaking in this regime

Utilizes recent bounds by F. Guerra relating to the Parisi solution

Abstract

We consider the Sherrington-Kirkpatrick model and we prove that the thermodynamic limit of the quenched free energy per site is strictly greater than the corresponding replica symmetric approximation, for all values of the temperature and of the magnetic field below the Almeida-Thouless line. This is based on recent rigorous bounds by F. Guerra, relating the true free energy of the system to the Parisi solution with replica symmetry breaking.