The present paper deals with the statistical mechanics of an asymmetrical Ising mounted on the Bethe lattice. An asymmetrical Ising model is defined by assuming the spin variable of the usual Ising Hamiltonian to take up the eigenvalues 1, − λ, where λ is an asymmetry parameter. It is shown...

Using a generalization of the VLP technique to spin-phonon systems the effect of spin-phonon interactions on the magnetic excitations of an S=1 Heisenberg ferromagnet having both exchange and single-ion anisotropy is studied. The calculations are carried out using a semi-invariant expansion of...

The critical behaviour of the generalized Ising model is studied using the power series coherent anomaly method. We work with the eleven-terms susceptibility series of Oitmaa and Enting. Taking the inverse of this series and studying the coherent anomalies we arrived at the results for Curie...

The zero-field high temperature static susceptibility series of the spin-S nearest-neighbour Ising model on simple cubic (SC), body-centred cubic (BCC) and face-centred cubic (FCC) lattices is thoroughly analysed by means of a power series coherent anomaly method (CAM). Our analysis revealed...

The magnetization of an anisotropic cubic spin-one Ising model with single-ion anisotropy is studied using a linear chain approximation. In particular, for several ratios, η, between the interchain and intrachain exchange interactions the critical temperatures of the second and first order...

Exact expressions for the Curie temperature, magnetization, quadrupolar moment and the susceptibility of a spin-one Ising model on a Bethe lattice are derived. Biquadratic exchange and single-ion anisotropy are included, in addition to the bilinear exchange interactions. The variation of the...

The continued fraction coherent anomaly method (CAM) is applied to study the criticality of the Blume-Capel model. For comparison, we present also the power series approach with a different way of calculating the critical coefficients. The variation of the Curie temperature Tc with respect to...

In this paper we present a detailed study of the physical properties of a non-Heisenberg spin model described by a Hamiltonian which consists of an usual bilinear coupling with the nearest-neighbour coupling constant J and a three-site interaction measured by a coupling constant L. This study is...

We calculate the dimension of the set which is complementary to the complete devil's staircase of a family of piecewise linear mappings. We obtain universal values of fractal dimension 12 for one region of the staircase and 0 for the remaining region. The ways by which these values are...

A variational calculation is given of an approximation scheme, which is far easier to apply than the cluster variation method, in the higher approximations. The Curie temperature of the Ising model in the square approximation in the present scheme is obtained as 2.6253 and 4.7611, respectively,...