A unified approach to the interpretation of displacive and order–disorder systems. I. Thermodynamical aspect

Some properties of a linear chain of harmonically coupled double wells are studied by the technique of the transfer operator. Exact values for the chain specific heat, the displacement probability density, and the first six even moments of the dynamical displacement correlation function are obtained. The model is shown to be a prototype for displacive as well as for order–disorder transitions depending on the strength of the harmonic coupling. Criteria for the harmonic behavior of the system are derived. By this method, it was not possible to find the exact form of the dynamical correlation functions for very anharmonic cases; this is so in general for order–disorder systems, but also for a small wave vector and temperature region in displacive systems.