Expansion in 1/z for the transition temperature and specific heat of ferromagnets

An expansion in powers of 1/z is used to study the effect of spin fluctuations on the transition temperature and specific heat of the Ising and Heisenberg models of ferromagnetism, for general spin s. The 1/z corrections to the Curie temperature TC agree with the cluster-expansion technique, which yields the same free energy and order parameter to first order in 1/z. For the Heisenberg model, the fluctuation correction to the specific heat contains a peak below TC. This peak is caused by the quantum fluctuations induced by the transverse degrees of freedom, which are absent from the Ising model. Specific-heat measurements in some materials may have found such a peak. As the spin s increases, the peak becomes better defined and decreases in temperature. In the classical limit s, the peak disappears and the fluctuation contributions in the Heisenberg and Ising models become identical below TC. The features of the Heisenberg model are very similar to those of a granular superconductor, where quantum fluctuations are induced by the charging energy and the classical limit is reached when the grain capacitance is infinite.