Stochastic Cutoff Method for Long-Range Interacting Systems

Abstract

A new Monte Carlo method for long-range interacting systems is presented. This method involves eliminating interactions stochastically with the detailed balance condition satisfied. When pairwise interactions V_ij of an N-particle system decrease with the distance as r_ij^−α, computational time per Monte Carlo step is O(N) for α≥d and O(N^2−α⁄d) for α<d, where d is the spatial dimension. We apply the method to a two-dimensional magnetic dipolar system. The method enables us to treat a huge system of 256² spins within a reasonable computational time, and reproduces a circular order originating from long-range dipolar interactions.