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physica status solidi (b)

A method for phase diagrams of spin‐1 Ising ferromagnetic systems

Hamza Polat, Ümit Akıncı, İ. Sökmen

Published Oct 9, 2003• 24 citations
Publisher

Abstract

Abstract A method in Ising models is introduced by using the effective field theory (EFT) with correlations. In the present method, for the spin‐1 Ising ferromagnetic systems with three coordination numbers q (q = 3, 4 and 6), we have derived a set of linear equations by taking as a basis the thermal averages of a central spin and a perimeter spin at the site i, which is defined within spin identities and differential operator technique. By solving numerically the set of linear equations derived individually for the Ising systems, we have evaluated the phase diagrams of both the spin‐1 Ising ferromagnetic systems with a single‐ion anisotropy and the spin‐1 transverse Ising ferromagnetic systems with a transverse field. The present results of critical transverse field for the spin‐1 transverse Ising systems improve those obtained by the pair approximation. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI
10.1002/pssb.200301858

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Abstract A method in Ising models is introduced by using the effective field theory (EFT) with correlations. In the present method, for the spin‐1 Ising ferromagnetic systems with three coordination numbers q (q = 3, 4 and 6), we have derived a set of linear equations by taking as a basis the thermal averages of a central spin and a perimeter spin at the site i, which is defined within spin identities and differential operator technique. By solving numerically the set of linear equations derived individually for the Ising systems, we have evaluated the phase diagrams of both the spin‐1 Ising ferromagnetic systems with a single‐ion anisotropy and the spin‐1 transverse Ising ferromagnetic systems with a transverse field. The present results of critical transverse field for the spin‐1 transverse Ising systems improve those obtained by the pair approximation. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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.
In this paper we investigate the effect of a random transverse field, distributed according to a trimodal distribution, on the phase diagram and magnetic properties of a two-dimensional lattice (square with z=4),  ferromagnetic Ising system consisting of magnetic atoms with spin-1. This study is done using the effectivefield theory (EFT) with correlations method. The equations are derived using a probability distribution method based on the use of exact Van der Waerden identities. We present our numerical results, such as the phase diagrams, the thermal variations of the transverse magnetization, the internal energy, the magnetic specific heat as a function of different values of p, the concentration of the random transverse field. As a result, the critical values of transverse field , temperature and concentration were obtained for the square lattice.
A new type effective field approach is used to derive the thermodynamical properties of the transverse Ising model. The method is based on an exact formal identity for the two-state transverse Ising model and utilizes an exponential operator technique. The lines of critical points in the Ω-T plane are derived and the critical transverse fields ΩC are obtained analytically, for lattices with coordination numbers z = 2, 4 and 6. This simple method yields results which represent a remarkable improvement on the usual mean field approximation. Our results are also compared with those from series expansion method.
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.