Application of computer algebra systems (CAS) to formal expansion of exact Callen equations into the systems of algebraic equations

Abstract

We present the application of computer algebra systems (CAS) to symbolic construction of algebraic equations describing different ordered as well as stochastic magnetic structures. We start with formal and exact, however non-tractable from the numerical point of view, Callen equations. Then, we apply the integral operator method (based on the integral representation of Dirac delta function) and use CAS to reformulate the related mathematical problem in terms of polynomial equations ready for numerical treatment. The complexity of the problem depends exponentially on coordination numbers of magnetic/nonmagnetic components, and by this, it makes the presented computer add approach the only possible method to treat complex multicomponent thin films and dilute multilayered structures. As two examples, we present the CAS add construction of related equations for binary alloys A^CB^1-C with structural disorder (Z^A = 2, Z^B = 4) and site-diluted thin film with n = 8 monatomic planes.