On the de Almeida--Thouless Transition Surface in the Multi-Species SK Model with Centered Gaussian External Field

We study the phase transition of the Parisi formula for the free energy in the multi-species Sherrington–Kirkpatrick model with a centered Gaussian external field and a positive-semidefinite variance profile matrix. We show that in terms of the strength of the external field and the variance profile, the de Almeida–Thouless surface delineates the boundary between replica symmetric solutions and replica symmetry breaking solutions.