PERCOLATION TECHNIQUES IN DISORDERED SPIN-FLIP DYNAMICS - RELAXATION TO THE UNIQUE INVARIANT MEASURE

We consider lattice spin systems with short range but random and unbou nded interactions. We give criteria for ergodicity of spin flip dynami cs and estimate the speed of convergence to the unique invariant measu re. We find for this convergence a stretched exponential in time for a class of ''directed'' dynamics (such as in the disordered Toom or Sta vskaya model). For the general case, we show that the relaxation is fa ster than any power in time. No assumptions of reversibility are made. The methods are based on relating the problem to an oriented percolat ion problem (contact process) and (for the general case) using a sligh tly modified version of the multiscale analysis of e.g. Klein (1993).