Phase Transitions

Abstract

This paper is concerned with the theory of those phase transitions which can be satisfactorily dealt with in terms of simple self-consistent equations. The transition itself can be thought of as arising from nontrivial (usually symmetry breaking) solutions of self-consistent equations. Phenomena falling into this category and reviewed below are ferromagnetism and antiferromagnetism, gas-liquid condensation, freezing, and superconductivity. Presumably many other phenomena can be similarly accounted for—ferroelectricity, superlattice formation, unmixing of solutions, etc.—but time does not permit discussion of all of these. Crystal phase transitions are probably of a more delicate variety and most likely cannot be handled in the rather crude approximations which seem so successful in the first class. Finally, a most unfortunate omission is the λ-point transition of liquid helium. This transition is associated with the Bose-Einstein condensation of the ideal gas, modified of course, by the interatomic interactions. It is not a transition of the type which falls naturally into the class which we have chosen to discuss.