One--Component Plasma of a Million Particles via angular--averaged Ewald potential: A Monte Carlo study

TL;DR

This study introduces an improved angular-averaged Ewald potential for simulating a one-component plasma, enabling more efficient Monte Carlo simulations of up to a million particles across various coupling strengths.

Contribution

We derived a correct, numerically efficient expression for the OCP energy using the original Ewald potential and demonstrated its effectiveness through large-scale Monte Carlo simulations.

Findings

Simulation efficiency increased by over two orders of magnitude.

Results agree with theoretical and previous numerical data.

Potential suitable for path integral Monte Carlo of electron gases.

Abstract

In this work, we derive a correct expression for the one--component plasma (OCP) energy via the angular--averaged Ewald potential (AAEP). Unlike E.~Yakub and C.~Ronchi (J. Low Temp. Phys. 139, 633 (2005)), who had tried to obtain the same energy expression from a two--component plasma model, we used the original Ewald potential for an OCP. A constant in the AAEP was determined using the cluster expansion in the limit of weak coupling. The potential has a simple form suitable for effective numerical simulations. To demonstrate the advantages of the AAEP, we performed a number of Monte--Carlo simulations for an OCP with up to a million particles in a wide range of the coupling parameter. Our computations turned out at least two orders of magnitude more effective than those with a traditional Ewald potential. A unified approach is offered for the determination of the thermodynamic limit in the whole investigated range. Our results are in good agreement with both theoretical data for a weakly coupled OCP and previous numerical simulations. We hope that the AAEP will be useful in path integral Monte Carlo simulations of the uniform electron gas.