Statistical Mechanics of Cooperative Phenomena

概要

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The method of attack developed by Kirkwood and Born-Green, whose application was almost exclusively confined to the theory of liquids, is applied to the statistical treatment of cooperative phenomena, by which we mean the order-disorder problem, its related phenomena and the hindered rotation in molecular crystals. Using Kirkwood's coupling parameter, we find an integral equation, which is simplified by a method of expansion. By a further simplification, we reach two kinds of integral equations, corresponding to Bragg-Williams' and Bethe's approximations respectively. In the case of nearest neighbour systems the latter equation is derived from a variational principle, which corresponds to the maximum condition of the partition function per interaction bond expressed in terms of the distribution function. According to our formulation Bethe's method of internal field and Fowler-Guggenheim's quasi-chemical method are derived from the same fundamental equation. This fact serves to clear undeartanding of the equivalence of these two points of view, although this equivalence is demonstrated by Fowler-Guggenheim by use of the grand canonical ensemble. It is further noted that from our variational formula we can attain to the extension of the variation method of Kramers-Wannier to the three-dimensional lattices. Thus, Kramers-Wannier's approximation proves to be only a metamorphosis of Bethe's approximation.
理論物理学刊行会の論文