An Exposition to Information Percolation for the Ising Model

Information percolation is a new method for analyzing stochastic spin systems through classifying and controlling the clusters of information-flow in the space-time slab. It yielded sharp mixing estimates (cutoff with an O(1)-window) for the Ising model on Z up to the critical temperature, as well as results on the effect of initial conditions on mixing. In this expository note we demonstrate the method on lattices (more generally, on any locally-finite transitive graph) at very high temperatures.