On the Theory of Cooperative Phenomena

We obtain the low temperature expansions of partition functions for several crystal types by direct counting of complexions and then discuss the typical cooperative phenomena. (1) Spontaneous magnetizations of the three dimensional Ising ferromagnets (in case of the simple cubic, the body centered cubic and the face centered cubic) are given. (2) Using the grand partition function for the face centered cubic lattice, the properties of the regular solution are discussed. We get there a condition for the appearance of an upper consolute temperature or a lower consolute temperature, taking account of the effects on free volume of each molecule due to the species of the nearest neighbor molecules. (3) Considering the regular solution as a mixture of holes and molecules, we are led to the properties of liquid. (4) Using the grand partition function for the triangular lattice, we discuss the adsorption phenomenon as the localized monolayer.