On the Almeida-Thouless transition line in the Sherrington-Kirkpatrick model with centered Gaussian external field

Abstract

We study the phase transition of the free energy in the Sherrington-Kirkpatrick mean-field spin glass model with centered Gaussian external field. We show that the corresponding Almeida-Thouless line is the correct transition curve that distinguishes between the replica symmetric and replica symmetry breaking solutions in the Parisi formula.