Cluster Monte Carlo study of magnetic dipoles

TL;DR

This paper develops and tests a cluster-update Monte Carlo algorithm for simulating two-dimensional magnetic dipoles, improving equilibration speed over traditional methods despite similar computational complexity.

Contribution

The paper introduces a combined cluster-update algorithm tailored for long-range, anisotropic dipole interactions in 2D XY-spin systems, enhancing simulation efficiency.

Findings

Faster system equilibration compared to Metropolis algorithm

Effective handling of long-range and anisotropic interactions

Comparable overall computational complexity

Abstract

We implement a cluster-update Monte Carlo algorithm to simulate magnetic dipoles of the XY-spin type confined in a two-dimensional plane. The long-range character and anisotropy in the dipole interaction are handled by using the Luijten-Bl\"ote algorithm and the Dotsenko-Selke-Talapov algorithm, respectively. We have checked the performance of this cluster-update algorithm in comparison to the Metropolis algorithm and found that it equilibrated the system faster in terms of the number of flipped spins, although the overall computational complexity of the problem remained the same.