First-order anharmonic correction to the free energy of a Coulomb crystal in periodic boundary conditions

The free energy of the classical one-component plasma is calculated analytically in the crystalline phase for both fcc and bcc lattices to O(${\mathit{T}}^2$), where T is the temperature. By application of thermodynamic perturbation theory, we explicitly evaluate the effect of three- and four-phonon interactions on the partition function. Periodic boundary conditions are applied to make contact with previous numerical work, in which the O(${\mathit{T}}^2$) term was assumed to be negligible. We find that it is much larger than previously thought. This increases the thermodynamic stability of the crystal phase over previous estimates.