Thermodynamics of~the~basic three-dimensional ferromagnetic models in~the~fluctuation approximation

R. R. Nigmatullin ; V. A. Toboev

Teoretičeskaâ i matematičeskaâ fizika, Tome 74 (1988) no. 1, pp. 112-124

Résumé

On the basis of the approximation which consists of replacing the operator of the square of the fluctuation components of the local field by its mean value $(\Delta\sigma_f^\alpha)^2\simeq\langle(\Delta\sigma_f^\alpha)^2\rangle$, $\Delta\sigma_f^\alpha=\sigma_f^\alpha-\langle\sigma_f^\alpha\rangle$ (called henceforth the static fluctuation approximation), a systematic microscopic scheme is proposed for calculating the correlation functions and the thermodynamic characteristics associated with them for a large class of magnetic systems. The basic threedimensional ferromagnetic models (Ising, Heisenberg) are studied fairly fully and from a common point of view in zero magnetic field for temperatures $T\geqslant T_c$. The critical temperatures of the models are determined, and the specific heat and binary correlation functions of the short-range order are calculated for the three basic types of cubic lattice with short-range interaction. Comparison of the obtained results with other methods of calculating the models indicates a good accuracy of the approximation, which may provide a reliable basis for the calculation of more complicated systems. Ways of testing experimentally the fluctuation approximation in the paramagnetic region of temperatures are pointed out.