A study of a local Monte Carlo technique for simulating systems of charged particles

TL;DR

This paper evaluates a local Monte Carlo method for simulating charged particle systems, demonstrating its efficiency and accuracy across various temperatures and analyzing factors influencing its sampling performance.

Contribution

It introduces and assesses a local lattice Monte Carlo technique for charged particles, highlighting its efficiency and the role of charge mobility in sampling.

Findings

High accuracy achieved over a large temperature range

Charge mobility is maximized at low plaquette update rates

Uniform electric field sampling impacts simulation efficiency

Abstract

We study some aspects of a Monte Carlo method invented by Maggs and Rossetto for simulating systems of charged particles. It has the feature that the discretized electric field is updated locally when charges move. Results of simulations of the two dimensional one-component plasma are presented. Highly accurate results can be obtained very efficiently using this lattice method over a large temperature range. The method differs from global methods in having additional degrees of freedom which leads to the question of how a faster method can result. We argue that efficient sampling depends on charge mobility and find that the mobility is close to maximum for a low rate of independent plaquette updates for intermediate temperatures. We present a simple model to account for this behavior. We also report on the role of uniform electric field sampling using this method.