Comparison of the clock, stochastic cutoff, and Tomita Monte Carlo methods in simulating the dipolar triangular lattice at criticality

TL;DR

This study compares the efficiency of clock, stochastic cutoff, and Tomita Monte Carlo methods against traditional Metropolis in simulating dipolar triangular lattices at criticality, highlighting improvements with specific optimizations.

Contribution

It provides a comparative analysis of three advanced Monte Carlo methods and demonstrates how certain optimizations enhance their performance over standard approaches.

Findings

Optimized methods outperform unoptimized versions near criticality.

Incorporating boxing nearby neighbors and overrelaxation improves efficiency.

These methods are more suitable than Metropolis with overrelaxation when optimized.

Abstract

Magnetic nanostructures find application in diverse technological domains and their behavior is significantly influenced by long-range dipolar interactions. However, simulating these systems using the traditional Metropolis Monte Carlo method poses high computational demand. Several methods, including the clock, stochastic cutoff, and Tomita approaches, can reduce the computational burden of simulating 2D systems with dipolar interactions. Although these three methods rely on distinct theoretical concepts, they all achieve complexity reduction by a common strategy. Instead of calculating the energy difference between a spin and all its neighbors, they evaluate the energy difference with only a limited number of randomly chosen neighbors. This is achieved through methods like the dynamic thinning and Fukui-Todo techniques. In this article, we compared the performance of the clock, SCO, Tomita, and Metropolis methods near the critical point of the dipolar triangular lattice to identify the most suitable algorithm for this type of simulation. Our findings show that while these methods are less suitable for simulating this system in their untuned implementation, incorporating the boxing nearby neighbors method and overrelaxation moves makes them significantly more efficient and better suited than the Metropolis method with overrelaxation.