A message-passing scheme for non-equilibrium stationary states

作者：Aurell Erik^*; Mahmoudi Hamed

来源：Journal of Statistical Mechanics: Theory and Experiment , 2011, P04014.

DOI：10.1088/1742-5468/2011/04/P04014

• cavity and replica method

We study stationary states in a diluted asymmetric (kinetic) Ising model. We apply the recently introduced dynamic cavity method to compute magnetizations of these stationary states. Depending on the update rule, different versions of the dynamic cavity method apply. We here study synchronous updates and random sequential updates, and compare local properties computed by the dynamic cavity method to numerical simulations. Using both types of updates, the dynamic cavity method is highly accurate at high enough temperatures. At low enough temperatures, for sequential updates the dynamic cavity method tends to a fixed point, but this does not agree with numerical simulations, while for parallel updates, the dynamic cavity method may display oscillatory behavior. When it converges and is accurate, the dynamic cavity method offers a huge speed-up compared to Monte Carlo, particularly for large systems.

• 出版日期2011-4