We study the spin-1 Blume–Capel model under a random crystal field in the tridimensional semi-infinite case. This has been done by using the real-space renormalization group approximation and specifically the Migdal–Kadanoff technique. Interesting results are obtained, which tell us that the...

In the present work we study the critical properties of the ferromagnetic three-color Ashkin–Teller model (3AT) by means of a Migdal–Kadanoff renormalization group approach on a diamond-like hierarchical lattice. The analysis of the fixed points and flux diagram of the recursion relations is...

The two-dimensional ferromagnetic anisotropic Ashkin–Teller model is investigated through a real-space renormalization-group approach. The critical frontier, separating five distinct phases, recovers all the known exact results for the square lattice. The correlation length (νT) and crossover...

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...

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...

The critical behaviour of thin films containing quenched random impurities and inhomogeneities is investigated by the renormalization-group method to the one-loop order within the framework of the n-component φ4-model. The finite-size crossover in impure films has been considered on the basis...

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,...

Using a real-space renormalization group procedure with no adjustable parameters, we investigate the Blume-Emery-Griffiths model on the square lattice. The formalism respects sublattice symmetry, allowing the study of both signs of K, the biquadratic exchange coupling. Our results for K 0 are...

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...

Phase diagrams of the micromaser system are mapped out in terms of the physical parameters at hand like the atom cavity transit time τ, the atom–photon frequency detuning Δω, the number of thermal photons nb and the probability a for a pump atom to be in its excited state. Critical...