Dynamical TAP equations for non-equilibrium Ising spin glasses

Abstract

We derive and study dynamical TAP equations for Ising spin glasses obeyingboth synchronous and asynchronous dynamics using a generating functionalapproach. The system can have an asymmetric coupling matrix and the externalfields can be time-dependent. In the synchronously updated model, the TAPequations take the form of self-consistent equations for magnetizations at timet + 1, given themagnetizations at time t. In the asynchronously updated model, the TAP equations determine the time derivativesof the magnetizations at each time, again via self-consistent equations, given the currentvalues of the magnetizations.