A Cavity Master Equation for the continuous time dynamics of discrete   spins models
  We present a new method to close the Master Equation representing the continuous time dynamics of Ising interacting spins. The method makes use of the the theory of Random Point Processes to derive a master equation for local conditional probabilities. We analytically test our solution studying two known cases, the dynamics of the mean field ferromagnet and the dynamics of the one dimensional Ising system. We then present numerical results comparing our predictions with Monte Carlo simulations in three different models on random graphs with finite connectivity: the Ising ferromagnet, the Random Field Ising model, and the Viana-Bray spin-glass model. 
Erik Aurell, Gino Del Ferraro, Eduardo Dominguez, Roberto Mulet
cond-mat.dis-nn cond-mat.stat-mech