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

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.