Dynamical TAP equations for non-equilibrium Ising spin glasses

Details Dynamical TAP equations for non-equilibrium Ising spin glasses Dynamical TAP equations for non-equilibrium Ising spin glasses

2011-03-05

arxiv.org/abs/1103.1044v1

J. Stat. Mech. (2011) P03031

Physics

Condensed Matter

Disordered Systems and Neural Networks

accepted for publication in JSTAT

Scientific paper

10.1088/1742-5468/2011/03/P03031

We derive and study dynamical TAP equations for Ising spin glasses obeying both synchronous and asynchronous dynamics using a generating functional approach. The system can have an asymmetric coupling matrix, and the external fields can be time-dependent. In the synchronously updated model, the TAP equations take the form of self consistent equations for magnetizations at time $t+1$, given the magnetizations at time $t$. In the asynchronously updated model, the TAP equations determine the time derivatives of the magnetizations at each time, again via self consistent equations, given the current values of the magnetizations. Numerical simulations suggest that the TAP equations become exact for large systems.

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