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Physica Scripta

Critical properties of a quantum spin-1/2 random-bond model

Carla Buzano

Published Jun 1, 1991• 1 citation
Publisher

Abstract

We investigate a model which differs from the Ising model in transverse field with random-bonds by the addition of an interaction term in transverse direction. Such a model is analyzed by the effective Hamiltonian method extended to random system. The critical properties of the system are considered and the phase diagram is derived. The role of the transverse interaction term is examined.

DOI
10.1088/0031-8949/43/6/015

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We investigate a model which differs from the Ising model in transverse field with random-bonds by the addition of an interaction term in transverse direction. Such a model is analyzed by the effective Hamiltonian method extended to random system. The critical properties of the system are considered and the phase diagram is derived. The role of the transverse interaction term is examined.
Abstract Within effective field theory (EFT), the critical properties of a random transverse crystal field Ising model with bond dilution are studied on a square lattice. Under both weak and strong bond dilution conditions, we consider three cases (α = 0,±0.5) of a transverse crystal field ratio, obtaining global phase diagrams in T−D x space for changes in the random transverse crystal field concentration. The phase diagrams obtained for a weak bond dilution are very similar in shape to those of pure bond but with decreases in corresponding ordered phases and critical values. However, the phase diagrams for a strong bond dilution exhibit varieties, including a change in reentrant phenomenon, the occurrence of transverse crystal field degeneration, and the opposite direction crossover of temperature peak value.
The ferromagnetic-phase stability limit and magnetization of a quenched bond-mixed spin-1/2 transverse Ising model in an anisotropic simple square lattice are studied within the framework of an effective-field theory considering both competing and noncompeting interactions. In the bond-disordered case, where bonds J1{J}_{1}J1​ and J2{J}_{2}J2​ occur with probabilities 1-p and p, respectively, critical curves are obtained for various \ensuremath{\alpha}'s (\ensuremath{\alpha}\ensuremath{\equiv}J1{J}_{1}J1​/J2{J}_{2}J2​), and the critical bond concentrations pc{p}_{c}pc​ at which the ferromagnetic phase breaks down are determined. As \ensuremath{\alpha}\ensuremath{\rightarrow}0, the mixed model reduces to the diluted Ising model and the results obtained are compared to those available in the literature. The effect of the transverse field (for different \ensuremath{\alpha}'s) in the thermal behavior of the magnetization as a function of the concentration is also discussed.