Application of computer algebra systems (CAS) to symbolic construction of coupled equations for magnetic susceptibility of amorphous systems with different coordination numbers

Abstract

We present the application of computer algebra systems to symbolic construction of two coupled systems of equations obtained from the exact Callen equation for a set of magnetizations and relevant magnetic susceptibilities in the case of complex amorphous ternary and binary diluted alloys like (ApB1-p)xC1-x with concentrations p and x, and different coordination numbers. The present paper is an extension of our previous one (Annales UMCS Informatica AI 5, 2006, 93) where the systems of polynomial equations for spontaneous magnetizations without external magnetic field have been obtained. Now, we introduce the external magnetic field and determine with the use of CAS full system of equations for both local magnetic susceptibilities and local magnetizations concerning all components of the complex magnetic systems. Finally, the numerical solutions of constructed coupled equations are found and discussed. The special attention is paid to the ferromagnetic region where the existence of low-temperature ordering transition, below the usual Curie phase transition, is searched as an interesting phenomenon from the technical point of view. The presented CAS added description can be understood as automatic constructor-simulator of relevant properties of amorphous alloys when the parameters of the system in question form an input to the described CAS-package.