Parallelized Stochastic Cutoff Method for Long-Range Interacting Systems

We present a method to parallelize the stochastic cutoff (SCO) method, which is a Monte-Carlo method for long-range interacting systems. After interactions are eliminated by the SCO method, we subdivide the lattice into non-interacting interpenetrating sublattices. This subdivision enables us to parallelize Monte-Carlo calculation in the SCO method. Such subdivision is found by numerically solving the vertex coloring of a graph created by the SCO method. We use an algorithm proposed by Kuhn and Wattenhofer to solve the vertex coloring by parallel computation. The present method was applied to a two-dimensional magnetic dipolar system on an $L\times L$ square lattice to examine its parallelization efficiency. The result showed that, in the case of L=2304, the speed of computation increased about 102 times by parallel computation with 288 processors.