An Iterative Construction of Solutions of the TAP Equations for the Sherrington-Kirkpatrick Model

Abstract

We propose an iterative scheme for the solutions of the TAP-equations in the Sherrington-Kirkpatrick model which is shown to converge up to and including the de Almeida-Thouless line. The main tool is a representation of the iterations which reveals an interesting structure of them. This representation does not depend on the temperature parameter, but for temperatures below the de Almeida-Thouless line, it contains a part which does not converge to zero in the limit. © 2013 Springer-Verlag Berlin Heidelberg.