Parallelized Stochastic Cutoff Method for Long-Range Interacting Systems

TL;DR

This paper introduces a parallelization technique for the stochastic cutoff method, enabling efficient Monte-Carlo simulations of long-range systems by subdividing the lattice into non-interacting parts, significantly boosting computational speed.

Contribution

The paper develops a parallelization approach for the SCO method using graph vertex coloring and demonstrates its effectiveness on large magnetic systems.

Findings

Achieved 102-fold speedup with 288 processors for a 2304x2304 lattice.

Successfully parallelized the SCO method using vertex coloring algorithms.

Validated the method on a two-dimensional magnetic dipolar system.

Abstract

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.