Extension of the high-temperature, free-energy series for the classical vector model of ferromagnetism in general spin dimensionality

The authors present the results of a study of the free energy and specific heat of the classical vector model of ferromagnetism. High-temperature series for the free energy are presented as far as the 12th term in general spin dimensionality (D) and the 13th term for the case D=3. The techniques used to derive these series are discussed in some detail. The general series is shown to reduce to that for the Ising Model for D=1, and to agree with the expansion of the exact result for the spherical model for the case D= infinity . The cases D=2 and D=3 correspond to the classical planar and classical Heisenberg models, respectively. It is demonstrated that the general series reproduces previous results for both of these models, with the exception of a small disagreement with the calculated 11th terms of Ferer et al. (1971, 1973). In addition, the general series extends the series for each of these models by one term, and independent work for D=3 provides one further term.