The statistical mechanics of a liquid of two-state molecules

The question of how the internal degrees of freedom of molecules are influenced by, and themselves influence, a condensed phase is taken up for the special case of a liquid of two-state molecules. It is well known that this model, in its classical version, is immediately solvable within a number of many-body approximations when the system is treated as a mixture. However, by using an internal-degree-of freedom diagrammatic approach, the fact that one can remove the internal dynamics and consider the system either as if it had an effective density or as if it were subject to effective interactions is made manifest. Further, by considering the analogy to magnetic systems, one is forced to predict, at least formally, the existence of a phase transition which implies a cooperative condensation into one particular internal state. The quantum mechanical version of the problem is then solved similarly (with a discretized path integral method) but the effective density and interaction are generalized to matrices and the classical phase transition becomes that of a quantal spin system. In the course of the discussion, both the classical and quantal ideas are shown to have some relevance to a number of physical problems; including the behavior of polarizable molecules, the structure of molten salts, and the symmetrization of hydrogen bonds.