The general-spin Blume–Capel model is studied by using an effective-field theory with correlation. An expression for the free energy within the effective-field theory is proposed, and the complete phase diagram is constructed in the temperature and single-ion anisotropy plane. The first-order...

The variational approach based on the Bogoliubov inequality for the free energy is used to study the three-dimensional anisotropic Heisenberg XXZ model with a crystal field. The magnetization and the phase diagrams are obtained as a function of the parameters of the Hamiltonian. Limiting cases,...

The vectorial generalization of the Blume–Emery–Griffiths model, proposed by Berker and Nelson to describe the behavior of films of 3He–4He mixtures, is studied by Monte Carlo simulations on the triangular lattice. The temperature versus chemical potential plane phase diagram, for a...

We investigate the Hamiltonian dynamics of two low-dimensional quantum spin systems in a random field, at the infinite-temperature limit: the XY chain and the two-leg XY ladder with interchain Ising interactions. We determine the longitudinal spin autocorrelation functions of the spin-12XY chain...

The criticality of the quantum anisotropic spin-12 Heisenberg antiferromagnetic model is studied by the mean-field renormalization group (MFRG) approach. The critical temperature and the thermal exponent for the ferromagnetic (F) and antiferromagnetic (AF) cases are obtained as a function of the...

The spin-σ Ising model with diluted and symmetric random crystal field is studied for σ⩾1 in the pair approximation based on Bogoliubov inequality for the free energy. Global phase diagrams are obtained in the temperature versus crystal field plane for the whole range of concentration in the...

It is shown that the recently proposed finite size scaling renormalization group, when using systems infinite in one dimension and finite in the others, is equivalent to the Nightingale (correlation length) phenomenological renormalization. The equivalence, however, is concerned only with the...

The phase diagram and the temperature dependence of the magnetization of the random-site binary ferromagnetic Ising model consisting of spin-12 and spin-1 components in the presence of crystal-field interactions is investigated by the use of a mean field theory. By considering in this simple...

The simple quadratic Ising model with nearest- and next-nearest-neighbor interactions is investigated by means of the mean field renormalization group approach. By conveniently choosing the size of the blocks one obtains the expected phase diagram exhibiting ferromagnetic, antiferromagnetic,...

The critical properties of the d-dimensional mixed-spin model (σ =12 and S = 1) is studied by using the mean-field renormalization group. The phase diagram and estimates of the critical exponent are obtained. Results are compared with other types of calculations when available.