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 of 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 Γ the Debye-Huckel result for F_ex and U_ex is recovered. For Γ ? 1, these depend linearly on Γ in accordance with the Monte Carlo findings for the OCP. The MC data for the internal energy are reproduced fairly well by the expression for U_ex obtained.