Auxiliary field simulation and Coulomb's Law

TL;DR

This paper reviews local algorithms for simulating charged particles, including molecular dynamics and Monte-Carlo methods, focusing on handling long-range Coulomb interactions efficiently.

Contribution

It introduces a local Monte-Carlo algorithm for Coulomb interactions and compares its efficiency with molecular dynamics approaches.

Findings

Local algorithms enable simulation of charged particles with purely local dynamics.

The paper demonstrates how to incorporate Coulomb interactions into local Monte-Carlo methods.

Efficiency comparisons show the strengths of different simulation approaches.

Abstract

We review a family of local algorithms that permit the simulation of charged particles with purely local dynamics. Molecular dynamics formulations lead to discretizations similar to those of ``particle in cell'' methods in plasma physics. We show how to formulate a local Monte-Carlo algorithm in the presence of the long ranged Coulomb interaction. We compare the efficiencies of our molecular dynamics and Monte-Carlo codes.