Stochastic Cutoff Method for Long-Range Interacting Systems

TL;DR

The paper introduces a stochastic cutoff Monte Carlo method for efficiently simulating long-range interacting systems, reducing computational complexity while accurately capturing phenomena like dipolar-induced circular order.

Contribution

It presents a novel Monte Carlo approach that stochastically eliminates interactions, satisfying detailed balance, and adapts computational effort based on interaction decay rate.

Findings

Efficient simulation of large 2D dipolar systems with 65,536 spins.

Reproduction of circular order due to long-range dipolar interactions.

Computational time scales favorably for different decay exponents.

Abstract

A new Monte-Carlo method for long-range interacting systems is presented. This method consists of eliminating interactions stochastically with the detailed balance condition satisfied. When a pairwise interaction $V_{ij}$ of a $N$-particle system decreases with the distance as $r_{ij}^{-\alpha}$, computational time per one Monte Carlo step is ${\cal O}(N)$ for $\alpha \ge d$ and ${\cal O}(N^{2-\alpha/d})$ for $\alpha < d$, 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 $256^2$ spins with reasonable computational time, and reproduces a circular order originated from long-range dipolar interactions.