Internal energy of the classical two- and three-dimensional one-component-plasma

TL;DR

This paper reviews semi-phenomenological methods for estimating the internal energy of 2D and 3D one-component plasmas, introducing a hybrid approach that interpolates between weak and strong coupling regimes and comparing it with numerical data.

Contribution

It presents a hybrid semi-phenomenological approach for estimating the internal energy of 2D and 3D OCP, effectively interpolating between asymptotic limits and validated against numerical simulations.

Findings

Hybrid approach reproduces known asymptotes in weak and strong coupling limits.

Comparison shows the hybrid method's estimates are consistent with numerical data.

Discussion of KTHNY theory relates to melting transition in 2D OCP.

Abstract

We summarize several semi-phenomenological approaches to estimate the internal energy of one-component-plasma (OCP) in two (2D) and three (3D) dimensions. Particular attention is given to a hybrid approach, which reproduces the Debye-H$\ddot{\text{u}}$ckel asymptote in the limit of weak coupling, the ion sphere (3D) and ion disc (2D) asymptotes in the limit of strong coupling, and provides reasonable interpolation between these two limits. More accurate ways to estimate the internal energy of 2D and 3D OCP are also discussed. The accuracy of these analytic results is quantified by comparison with existing data from numerical simulations. The relevance of the KTHNY theory in locating melting transition in 2D OCP is briefly discussed.