Cell Theory of Classical Liquids. Phase Transition between Gas, Liquid and Solid. Part III. Yvon’s Method and its Generalization

Abstract

The Method, proposed by Yvon, to start with the cluster expansion formulae and to classify the contributions of the clusters according to the form of the figure showing the coordinates of particles in the summand is fully developed for uniform and non-uniform lattice systems and compared with the cluster variation method. The cell theory of liquids is investigated from the standpoint of this method. It is shown that the cell-pair approximation developed in Parts I and II from the stand-point of the cluster variation method is shown to be identical to the approximation in which the figures that are contained in a cell or a pair of cells are taken into account correctly and the others are neglected, again in our present standpoint.