Computational treatment of order-disorder processes by use of the cluster variation method

Abstract

We present an implementation of the cluster variation method (CVM), applied to the Ising model, for computational characterization of order-disorder processes in binary systems. We show how the Newton-Raphson iteration scheme (NRIS) is used for numerical solving of system of nonlinear equations, obtained from the condition of the free energy minimum within the framework of the CVM approximation. An emphasis is made on the problem of the starting iteration point (NRIS being very sensitive to the choise of this point), for obtaining the low-temperature ordered phases. It was shown that an infinitesimally small breaking of symmetry of the high-temperature disordered phases supresses finding solutions which correspond to the metastable phases (saddle points) by NRIS (below the critical temperature Tc). This kind of problem is illustrated by an example of oxygen ordering in basal planes of YBa2Cu3O6 + x system, modeled by the two-dimensional asymetric next-nearest neighbor Ising (ASYNNNI) model.