Comparison of theories of anharmonicity applied to a model of copper

We have applied five different formulations for the calculation of thermodynamic properties of an anharmonic crystal to a simple model of copper, in order to investigate the range of validity of each theory for a weakly anharmonic system. The theories used are the quasiharmonic approximation, anharmonic perturbation theory, self-consistent phonon theory, improved self-consistent phonon theory, and the cell model. We find that perturbation theory, improved self-consistent theory, and the cell model give comparable results up to half the melting temperature, with perturbation theory diverging slightly above this.