Diluted Ising Systems Research Articles

Self-Consistent Determination of the Distribution of Effective Field in Ising System

A more reasonable consistency condition, than the one adopted by Mamada and Takano, is proposed to determine the distribution of effective field in Ising system. The new condition modifies the equations of Mamada and Takano only slightly, but it gives far better values of the Curie temperature. The critical concentrations of dilute Ising system are found worse.

Statistical Mechanics of Quenched Solid Solutions with Application to Magnetically Dilute Alloys

The arrangement of atoms in solid solutions and alloys, prepared at high temperatures and cooled nonadiabatically, is not the one which is thermodynamically most stable. In establishing theories of phenomena related to the internal degrees of freedom of such a system, such as magnetism, one must be careful to account for this nonequilibrium distribution of atoms. In this paper, systems are treated with the aid of a fictitious equilibrium system. This fictitious system is constructed such that its thermal equilibrium properties are the same as the properties of the non-thermal-equilibrium system. Thus one can treat nonequilibrium systems by applying well known thermal equilibrium techniques to the fictitious system. The method is illustrated via the example of a magnetically dilute alloy. Brout's result for a very dilute Ising system is obtained with the aid of the theory of classical fluids, without collecting diagrams. A method for applying the higher approximations developed for classical fluids to the present problem is suggested; calculations and discussions of which are retained for a forthcoming paper.