A Semi-Phenomenological Theory of the Second Order Phase Transitions in Spin Systems. I

Abstract

A semi-phenomenological theory is developed on the basis of some assumptions in order to study the singularities of thermodynamic quantities in the vicinity of the Curie point. First, microscopic expressions are found for the coefficients in the expansion of the thermodynamic potential in terms of cumulants. Cumulants of all order are calculated in the one-dimensional Ising model, and the series expansion of the fourth order cumulant is also obtained in the two-dimensional Ising model. The three-dimensional Heisenberg model is also discussed, using the result of Rushbrooke et al. In all cases, the fourth order coefficient in the expansion of the thermodynamic potential tends to zero at the Curie points. And, in the last case, the eighth order coefficient diverges at the Curie point.