Determination of temperature of phase transition in magnetic alloys by branching theory methods

In this article a transcendental equation is obtained for the temperature T_c of the phase transition of a binary magnetic alloy by means of the cluster-variation method. The dependence of T_c on the exchange and crystallographic parameters, concentration, and coordination number is investigated. Particular cases are analyzed of a thinned and concentrated magnetic alloy. In the present article the cluster-variation method is employed to evaluate the dependence of concentration on the critical temperature of a magnetic binary alloy either with fixed or mobile atoms. A complete system of equations for the critical temperature can be obtained by using the branching theory [1]. When solving the equations, one finds that the equation which is written in terms of a determinant of a high order is the most difficult one. If one takes into account that the parameter of a near order depends on temperature (mobile atoms), then this increases the order of the determinant. The uses of symmetry enables one to lower considerably the order of the determinant in both cases,which makes it finally possible to solve the problem under consideration. The method yields qualitatively different results depending on whether the approximation is of fixed or mobile atoms (as previously noted, e.g., in [2]).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 107–112, May, 1978.