Abstract The transverse spin‐3/2 Ising model with random interactions is studied using an effective field method within the framework of a single‐site cluster theory. The effective field equations are derived using a probability distribution method based on the use of generalized Van der Waerden identities, that account exactly for the single‐site kinematic relations. A model is adopted in which the nearest‐neighbour exchange couplings are described by the probability distribution law: P(Jij) = p δ(Jij‐J) + (1‐p) δ(Jij‐aJ). The critical temperature at which the longitudinal magnetization vanishes is studied as a function of p and the transverse field strength. The thermal variation of the longitudinal and transverse magnetizations and higher‐order magnetization moments are also studied.
Site diluted spin-1/2 Ising and spin-1 Blume Capel (BC) models in the presence of transverse field interactions are examined by introducing an effective-field approximation that takes into account the multi-site correlations in the cluster of a considered lattice with an improved configurational averaging technique. The critical concentration below which the transition temperature reduces to zero is determined for both models, and the estimated values are compared with those obtained by the other methods in the literature. It is found that diluting the lattice sites by non magnetic atoms may cause some drastic changes on some of the characteristic features of the model. Particular attention has been paid on the global phase diagrams of a spin-1 BC model, and it has also been shown that the conditions for the occurrence of a second order reentrance in the system is rather complicated, since the existence or extinction of reentrance is rather sensitive to the competing effects between D/J, Ω/J and c.
Abstract Within the framework of the effective‐field theory with correlations, a spin‐$ {3 \over 2} $ transverse Ising model in the longitudinal random‐field on a honeycomb lattice is studied. The phase diagrams and the behavior of the tricritical point are examined. The possible re‐entrance phenomena displayed by the system due to the competition effects that occur for the appropriate ranges of the random and transverse field are investigated. The longitudinal and transverse magnetizations, the longitudinal quadrupolar moments and internal energy are given numerically for a honeycomb lattice (z = 3). (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A finite cluster effective-field theory in which the single-site kinematic relations are treated exactly is applied to a study of the spin-one Ising ferromagnet on a honeycomb lattice. The Ising model studied contains both biquadratic exchange, J′ and single-ion anisotropy D in addition to the usual bilinear exchange interactions J. The second-order phase boundary is studied for a range of interaction strengths and the results compared to those of other methods. The dependence of the results on cluster size is investigated. The magnetization predicted by the four-site cluster theory for a selection of single-ion anisotropy strengths is also compared with exact results that have recently been deduced in the subspace J′/J=−[ln cosh(βJ)]/(βJ). In extending the theory to account for site dilution, a form of configurational averaging is adopted that is superior to that of earlier authors. The variation with site dilution of the tricritical point in the T-D plane is reported.
Phase diagrams and the thermal variations of the order‐parameters in the mixed spin‐1 and spin‐
23 ising model on the Bethe lattice
Abstract The mixed spin‐1 and spin‐
23 Blume‐Capel Ising ferromagnetic system (J > 0) with two crystal‐field interactions, DA for spin‐1 and DB for spin‐
23, is studied on the Bethe lattice using the exact recursion equations for the central‐spin with spin‐
23. The exact expressions for the order‐parameters, the Curie temperature and the free energy are obtained in terms of the recursion relations. The phase diagrams on the
(JkTc,JDA) and
(JkTc,JDB) planes are studied for selected values of DB/J and DA/J, respectively, for the coordination numbers q = 3, 4, and 6. Besides the second‐order phase transition lines, the lines of the first‐order phase transitions terminating either at a tricritical point or at an isolated critical point are found. The thermal variations of the order‐parameters are studied with two formulations, both obtained on the Bethe lattice for the mixed spin‐1 and spin‐
23 Ising system using the exact recursion relations, but one with the central‐spin with spin‐1 and the other is for the central‐spin with spin‐
23 for q = 3, thus, it is shown that the choice of the central‐spin on the Bethe lattice has no effect on the phase diagrams.