This paper systematically studies and improves the statistical theory of the kink-phonon interactive mixture in a one-dimensional model for the displacive phase transition. By taking applicable forms of the path integral for both the partition functions of kink and phonon and altering the method in calculating the path integral of phonon, a more reasonable and general expression of the partition function of the Grand ensemble is obtained. Under the lowest eigenstate approximation, the Grand.partition function may be reduced to a result similar to that of reference[6]. Under the classical approximation, the average density of the kink calculated from the Grand partition function is in agreement with the result of the computer simulation better than those obtained in earlier publications.
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