Local Simulation Algorithms for Coulombic Interactions

TL;DR

This paper introduces a local Monte Carlo algorithm for simulating Coulombic interactions that avoids explicit pair potential calculations or solving the Poisson equation, enhancing efficiency in charged system simulations.

Contribution

It presents a novel local simulation algorithm for Coulomb interactions based on dynamically constrained Monte Carlo dynamics, with improved efficiency through cluster methods.

Findings

Efficient local algorithm for charged systems

No need for pair potential evaluation

Enhanced performance with cluster methods

Abstract

We consider dynamically constrained Monte-Carlo dynamics and show that this leads to the generation of long ranged effective interactions. This allows us to construct a local algorithm for the simulation of charged systems without ever having to evaluate pair potentials or solve the Poisson equation. We discuss a simple implementation of a charged lattice gas as well as more elaborate off-lattice versions of the algorithm. There are analogies between our formulation of electrostatics and the bosonic Hubbard model in the phase approximation. Cluster methods developed for this model further improve the efficiency of the electrostatics algorithm.