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.