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physica status solidi (b)

A New Type of Bond‐Dilution Problem in a Ferromagnetic Insulator with a Fractional Random Coordination Number

Enaldo F. Sarmento, Heber R. da Cruz, T. Kaneyoshi

Published Feb 1, 1989• 0 citations
Publisher

Abstract

Abstract The ferromagnetic phase stability limits (or phase diagrams) of a quenched bond‐diluted spin‐ ½ transverse Ising ferromagnetic insulator with a fractional random coordination number are studied within the framework of the effective‐field theory with correlations. The changes of transition temperature and critical concentration with the topology of the network (or the averaged connectivity) are examined in the zero transverse field. The results obtained are compared with those available in the literature. The influences of transverse field on the critical frontiers are also obtained.

DOI
10.1002/pssb.2221510228

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Abstract The ferromagnetic phase stability limits (or phase diagrams) of a quenched bond‐diluted spin‐ ½ transverse Ising ferromagnetic insulator with a fractional random coordination number are studied within the framework of the effective‐field theory with correlations. The changes of transition temperature and critical concentration with the topology of the network (or the averaged connectivity) are examined in the zero transverse field. The results obtained are compared with those available in the literature. The influences of transverse field on the critical frontiers are also obtained.
Abstract The bond‐dilution effects on the phase diagram of a spin‐1 king ferromagnet in a transverse field with random longitudinal field is investigated within an expansion technique for cluster identities of spin‐ localized spin systems. Longitudinal and transverse magnetizations are studied for several values of thc bond concentration. The critical temperature dependence on the bond concentration, the longitudinal field, and the transverse field are presented. General formulae applicable to structurcs with arbitrary coordination number N are given.
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.
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 effect of random bond (site) dilution on the phase transition of a three-dimensional transverse Ising model is studied by a cluster variation, along with perturbation expansion method. Complete phase diagrams in the temperature-concentration-transverse-field space are constructed for both the cases. The value of critical transverse field as a function of concentration, at zero temperature, exhibits a discontinuity at the critical value of concentration for the existence of phase transition, as conjectured by Harris. As is expected for the existence of a second-order phase transition, the static susceptibility diverges on the critical surface.