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The thermodynamic Green function of a weak anharmonic crystal, obtained through the equation of motion method, has been used to derive an explicit expression for the interaction energy. The Helmholtz free energy (F) has been obtained by integrating this interaction energy over a formal coupling parameter. Under certain conditions the expression for F has been shown to be identical with that obtained from perturbation theory and diagrammatic methods.
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Shukla et al. (1971) studied this question.
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