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Communications in Theoretical Physics

Phase Diagrams of a Transverse Ising Model with Interfaces

Zhou JianHua, Yang ChuanZhang

Published Jul 30, 1999• 0 citations
Publisher

Abstract

A transverse Ising model for a magnetic superlattice of spin-1/2 Ising layered media intercalated by periodic interfaces described by the spin-1/2 Ising model is considered. Phase diagrams and different profiles of magnetization determined by the parameters of the model are discussed within a variational procedure based on Bogoliubov's inequality for the free energy. Our results agree to those of the other's work at the limit of .

DOI
10.1088/0253-6102/32/1/67

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A transverse Ising model for a magnetic superlattice of spin-1/2 Ising layered media intercalated by periodic interfaces described by the spin-1/2 Ising model is considered. Phase diagrams and different profiles of magnetization determined by the parameters of the model are discussed within a variational procedure based on Bogoliubov's inequality for the free energy. Our results agree to those of the other's work at the limit of .
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The phase diagrams of spin-1/2 Ising model on a two-layer Bethe lattice with antiferromagnetic interactions for each layer and either antiferromagnetic or ferromagnetic interaction between the layers are investigated by using the pairwise approach for given values of coordination number q.The exact expressions of the order--parameters, response functions and free energy are obtained in terms of the recursion relations.The ground-state phase diagrams are calculated for given system parameters of the model.In the guidance of the ground-state phase diagrams, the temperature dependent phase diagrams of the model are also studied in detail for given coordination numbers q = 3, 4 and 6.It was found that the system presents only second-order phase transitions with different thermal behaviors for all values of q.In addition, two Néel temperatures, T N , are found for q = 6 only.
The ferromagnetic spin-2 quantum Blume-Capel model in the presence of a transverse crystal field interaction is studied by employing a variational approach based on Bogoliubov inequality for the free energy and an exact mapping of the ground state. The thermodynamic properties have been obtained using a single spin cluster, which is equivalent to the usual mean-field approximation. The temperature dependence of the magnetization has been analyzed and the global phase diagram, as function of the model parameters, has been obtained for any values of the coordination number of the lattice. A variety of quantum phase transitions, multiple and multicritical points, are present in several topologies of the corresponding phase diagrams. The ground state properties of the system have also been obtained through an exact mapping of the spin-2 model onto another equivalent spin-1 Blume-Capel model in a transverse field. This mapping allows one to determine an exact asymptote formula of the phase diagram at zero temperature in the limit of large longitudinal crystal field for any lattice dimension.
The effect of surface and bulk transverse fields on the phase transitions of a semi-infinite spin-1 ferromagnetic Ising model is investigated within a finite cluster approximation with an expansion technique for cluster identities of spin-1 localized spin systems. The phase diagrams are determined as a function of the ratio of bulk and surface transverse fields, the temperature and the transverse field of the surface. They show that the systems exhibit a variety of phase transitions. A dead layer is also obtained in a special region of space parameters.
We investigate phase transitions in the Ising model and the ANNNI model in transverse field using the interface approach. The exact result of the Ising chain in a transverse field is reproduced. We find that apart from the interfacial energy, there are two other response functions which show simple scaling behavior. For the ANNNI model in a transverse field, the phase diagram can be fully studied in the region where a ferromagnetic to paramagnetic phase transition occurs. The other region can be studied partially; the boundary where the antiphase vanishes can be estimated.