The spin-32 Ising model Hamiltonian with arbitrary bilinear (J) and biquadratic (K) pair interactions is studied by using the lowest approximation of the cluster variation method (LACVM) and the path probability method (PPM) with the point distribution. First, equilibrium properties of the model...

A new mean-field approximation is proposed for the sandpile model of Bak, Tang and Wiesenfeld and the distribution of heights in the self-organized critical state is calculated. We treat several series of successive topples to approximate various avalanches. In contrast to the previous...

The magnetic properties of the mixed spin-12 and spin-1 Ising ferromagnetic system with a crystal–field interaction in the absence and presence of an external magnetic field are studied by using the cluster variation method. Thermal variations of order parameters are investigated and the...

The cluster variation method is applied to study critical properties of the Potts-like ferromagnetic anisotropic exchange interaction model. Phase transition temperatures, order parameter discontinuities and latent heats of the model on the triangular and the fcc lattices are determined by the...

We investigate the temperature dependence of the order parameters of the Blume–Capel model for zero magnetic field in the lowest approximation of the cluster variation method which is identical to the mean-field approximation. Besides the stable branches of the order parameters, we establish...

The random-crystal field spin-1 Blume–Capel model is investigated by the lowest approximation of the cluster-variation method which is identical to the mean-field approximation. The crystal field is either turned on randomly with probability p or turned off with q=1−p in a bimodal...

We have analyzed relationship between two parallel approaches to the cluster variation method (CVM) as a theoretical tool for studying statistical properties of binary systems. The first approach to the method uses the multisite correlation functions as variational variables, while the other...

The lattice gas model is examined to make a comparison between the superposition approximation and one which is free from the approximation as long as the three-body distribution is concerned. The formulation is applied to the type I superionic conductor, AgI, in which Ag-ions can move like the...

The multicritical behavior of the antiferromagnetic spin-32 Blume–Emery–Griffiths model in an external magnetic field is studied within the lowest approximation of the cluster variation method. We have investigated the thermal variations of order parameters for different values of...

The dynamic behaviour of the modified Pople–Karasz model is studied by the direct relaxation method and the path probability method. First the equilibrium behaviour of the model is given briefly in order to understand the dynamic behaviour. Then the direct relaxation method, which is based on...