Approximate methods for studying phase states in the Potts model of a dilute magnet
-
Semkin S.V.
Vladivostok State University of Economics and Service
Vladivostok. Russia -
Smagin V.P.
Vladivostok State University of Economics and Service
Vladivostok. Russia
The Potts model of a dilute magnet with an arbitrary number of states in an external field is considered. The aim of this paper is to study the critical behavior of this model. Three approximate methods have been used to study phase transitions in this model. The first method is the classical method of the mean field. Using this classical method of the mean field, the critical behavior of the diluted Potts magnet with an arbitrary number of states in a nonzero external field is analyzed. For a dilute Potts magnet, a modification of the mean field method is constructed, which coincides with the classical method for a pure magnet. This second method is a combination of the classical mean field and the binomial distribution by the number of occupied neighboring sites. It is found that the magnetic susceptibility in a zero external field near a critical temperature is a nonmonotonic concentration function and has a maximum at some value depending on the number of states of the Potts model and the coordination number of the lattice. The third method is a combination of averaging over local crystal fields and binomial distribution over the number of occupied neighboring sites. Each of these methods obtained such results. The dependence of the critical temperature on the external field and the concentration of magnetic atoms is constructed. A jump in the magnetization on a curve of phase transitions of the first order is found. A magnetic susceptibility has been obtained in the entire range of concentrations. The percolation thresholds for various lattices are found approximately. Comparison of the results with the previously known results is given. It is obtained that the coordinates of the end point of the phase transition line are monotonically increasing functions of the concentration of magnetic atoms.
Keywords: phase transitions, Potts model, dilute magnet.