A Cluster Controller for Transition Matrix Calculations

Abstract: We demonstrate that a temperature schedule for single-spin flip transition matrix calculations can be simply and rapidly generated by monitoring the average size of the Wolff clusters at a set of discrete temperatures. Optimizing this schedule yields a potentially interesting quantity related to the fractal structure of Ising clusters. We also introduce a technique in which the transition matrix is constructed at a sequence of discrete temperatures at which Wolff cluster reversals are alternated with certain series of single-spin flip steps. The single spin-flip transitions are then employed to construct a single transition matrix.