# Monte Carlo simulation of electrostatic interactions in inhomogeneous dielectric media: Correct sampling for the local lattice simulation algorithm

## TL;DR

This paper identifies and corrects a bias in a lattice Monte Carlo algorithm for simulating electrostatic interactions in inhomogeneous dielectrics, improving the physical accuracy of the simulations.

## Contribution

The authors introduce a parallel tempering approach to fix unphysical biases in the existing lattice Monte Carlo algorithm for dielectric media.

## Key findings

- Corrected the spurious attractive interactions in the original algorithm.
- Validated the improved method on binary mixtures and polymer solutions.
- Enhanced the physical realism of electrostatic simulations in inhomogeneous dielectrics.

## Abstract

We present a lattice Monte Carlo algorithm based on the one originally proposed by Maggs and Rossetto for simulating electrostatic interactions in inhomogeneous dielectric media. The original algorithm is known to produce attractive interactions between particles of the same dielectric constant in the medium of different dielectric constant. We demonstrate that such interactions are spurious, caused by incorrectly biased statistical weight arising from particle motion during the Monte Carlo moves. We propose a simple parallel tempering algorithm that corrects this unphysical bias. The efficacy of our algorithm is tested on a simple binary mixture and on an uncharged polymer in a solvent, and applied to salt-doped polymer solutions.