Free Energy of an Anharmonic Crystal

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Abstract
The perturbation techniques of statistical physics have been applied to obtain two formulas for the free energy of an anharmonic crystal. One involves an integration over the coupling constant and the other involves the exact Green's function; both are exact parallels of the fermion case. The anharmonic crystal differs from the interacting fermions in the structure of the phonon interaction, the effect of which on the perturbation series is carefully considered. The stationary property of the free energy with respect to the variation of the proper self-energy is proved. Expressions for the internal energy and entropy are also derived.

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