Equation of state of the one-component plasma derived from precision Monte Carlo calculations

Analytical fits to the one-component plasma (OCP) equation of state have been derived for internal energies that have reduced all N-dependent effects to within the statistical uncertainties introduced by the Monte Carlo computational process, which themselves are very small. Values of N≳500 adequately represent the thermodynamic limit. Using the fluid internal energies for only N=686, various analytical fits are generated, compared, and discussed. The thermal energy is accurately represented by a simple power-series fit with the leading term given by ${\Gamma }^{1/3}$, but also requires a small correction to the bcc Madelung term that brings that coefficient down to nearly -0.9, the value derived for hypernetted-chain theory. The fluid thermal energy data are reproduced to better than 0.2% over all Γ by our fit(s). The solid phase requires both anharmonic terms to be included in the fit, implying that the previous justification for dropping the first anharmonic correction is unwarranted. The location of the fluid-solid phase transition utilizing these new fits yields ${\Gamma }_{\mathrm{bcc}=178\mathrm{}}$ and ${\Gamma }_{\mathrm{fcc}=192\mathrm{}}$.