High-temperature expansions for classical spin models

The concepts of duality and broken symmetry are discussed briefly. It is shown how generalized colouring polynomials can be used to calculate the terms in a high-temperature expansion effectively. These results and those from two previous papers are used to obtain high-temperature series for a great variety of models. These are given explicitly for all models with two Boltzmann factors and for the Ashkin-Teller model. Many phase diagrams obtained from the series by Padé analysis are presented and their salient features discussed. A “principle” suggested by these phase diagrams is applied to the dilute Potts model.