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

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.