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 Gamma the Debye-Huckel result for F(ex) and U(ex) is recovered. For Gamma much greater than 1, 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 expression for U(ex) obtained.