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

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.