The effects of random crystal field on the stationary states of the kinetic spin-1 Blume Capel model are studied using the Glauber-type stochastic dynamics under the time-dependent oscillating field assumption. Our investigation, based on the equilibrium ground state phase diagram, revealed many...

We propose a stochastic model of interactive formation of individual expectations regarding the business climate in an industry. Our model is motivated by a business climate survey conducted since 1960 in Germany by the Ifo-institute (www.ifo.de). In accordance with the data structure of this...

The bond dilution Blume–Capel model with random crystal field is considered in the framework of the effective field theory. The expressions of magnetizations for honeycomb and square lattices are derived. Special emphasis is placed on thermodynamic properties of the two lattices and the...

We use the Migdal–Kadanoff renormalization group technique to study the spin-3/2 Blume–Capel model under a random crystal field, in the two- and three-dimensional cases. Studying the fixed points and the phase diagrams established, we find interesting results allowing us to understand the...

A new type of cluster theory in Ising models with an arbitrary spin S(S12) is presented by the use of the differential operator technique and Ising spin identities. The formulations for evaluating the transition line are derived for the two Ising systems with S=1 and 32 as well as for the spin-S...

The problem of order–order and order–disorder transitions in the system described by the 2D antiferromagnetic Blume–Capel model in the presence of a magnetic field is studied by the Wang and Landau flat-histogram simulation method and by the classical Monte Carlo. Anomalous thermodynamic...

A spin-1 Blume–Capel model with dilute and random crystal fields is examined for honeycomb and square lattices by introducing an effective-field approximation that takes into account the correlations between different spins that emerge when expanding the identities. For dilute crystal fields,...