Accurate first-principle equation of state for the One-Component Plasma

TL;DR

This paper derives accurate first-principle expressions for the excess free energy and internal energy of the classical one-component plasma using the Hubbard-Schofield transformation, matching Monte Carlo data across plasma parameters.

Contribution

It introduces a novel analytical approach to compute the equation of state for the OCP by mapping it onto an Ising-like Hamiltonian and using the ideal gas as a reference.

Findings

Reproduces Debye-Huckel results at small plasma parameters

Matches Monte Carlo data for internal energy at large plasma parameters

Provides explicit analytical expressions for $F_{ex}$ and $U_{ex}$

Abstract

Accurate "first-principle" expressions for the excess free energy $F_{ex}$ and internal energy $U_{ex}$ of the classical one-component plasma (OCP) are obtained. We use the Hubbard-Schofield transformation that maps the OCP Hamiltonian onto the Ising-like Hamiltonian, with coefficients expressed in terms of equilibrium correlation functions of a reference system. We use the ideal gas as a reference system for which all the correlation functions are known. Explicit calculations are performed with the high-order terms in the Ising-like Hamiltonian omitted. For small values of the plasma parameter $\Gamma$ the Debye-Huckel result for $F_{ex}$ and $U_{ex}$ is recovered. For large $\Gamma$ these depend linearly on $\Gamma$ in accordance with the Monte Carlo findings for the OCP. The MC data for the internal energy are reproduced fairly well by the obtained analytical expression.