An accurate equation of state for the one component plasma in the low coupling regime

TL;DR

This paper develops a highly accurate equation of state for the one component plasma in the low coupling regime by combining integral equations, Monte Carlo simulations, and analytical expressions, extending previous work on strongly coupled systems.

Contribution

It introduces a combined approach for accurately modeling the plasma's excess internal energy at low coupling, with precise analytical fits and consideration of finite size effects.

Findings

Accurate analytical fits of u(Γ) for 0 ≤ Γ ≤ 1 with precision ≥ 10^{-5}

Reliable results from HNC and asymptotic expressions only in narrow Γ intervals

Extension of previous Monte Carlo studies to low coupling regimes

Abstract

An accurate equation of state of the one component plasma is obtained in the low coupling regime $0 \leq \Gamma \leq 1$. The accuracy results from a smooth combination of the well-known hypernetted chain integral equation, Monte Carlo simulations and asymptotic analytical expressions of the excess internal energy $u$. In particular, special attention has been brought to describe and take advantage of finite size effects on Monte Carlo results to get the thermodynamic limit of $u$. This combined approach reproduces very accurately the different plasma correlation regimes encountered in this range of values of $\Gamma$. This paper extends to low $\Gamma$'s an earlier Monte Carlo simulation study devoted to strongly coupled systems for $1 \leq \Gamma \leq 190$ ({J.-M. Caillol}, {J. Chem. Phys.} \textbf{111}, 6538 (1999)). Analytical fits of $u(\Gamma)$ in the range $0 \leq \Gamma \leq 1$ are provided with a precision that we claim to be not smaller than $p= 10^{-5}$. HNC equation and exact asymptotic expressions are shown to give reliable results for $u(\Gamma)$ only in narrow $\Gamma$ intervals, i.e. $0 \leq \Gamma \lesssim 0.5$ and $0 \leq \Gamma \lesssim 0.3$ respectively.