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Journal of the Physical Society of Japan

Phase Diagrams of a Quenched Bond-Mixed Ising Ferromagnet with a Transverse Field

Enaldo F. Sarmento, T. Kaneyoshi

Published May 15, 1985• 12 citations
Publisher

Abstract

Using the ferromagnetic stability condition, the phase diagram is investigated in a quenched bond-mixed Ising ferromagnet with a transverse field \(\varOmega\) on the square lattice. The fact that large families of critical lines for negative-bond mixture meet at a single point on the line of T =0 is found to be closely related with frustrations due to negative bond. However the effect of frustrations may be observed only for a small value of \(\varOmega\) on the relevant physical properties.

DOI
10.1143/jpsj.54.1685

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Using the ferromagnetic stability condition, the phase diagram is investigated in a quenched bond-mixed Ising ferromagnet with a transverse field (\varOmega) on the square lattice. The fact that large families of critical lines for negative-bond mixture meet at a single point on the line of T =0 is found to be closely related with frustrations due to negative bond. However the effect of frustrations may be observed only for a small value of (\varOmega) on the relevant physical properties.
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 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.
The critical properties of the bond-diluted mixed spin-1/2 and spin-1 transverse Ising system with single-ion anisotropy are investigated by means of the effective field theory with correlations. Particular emphasis is given to the square lattice for which phase diagrams are obtained. If transverse field varies in the certain ranges we find that the tricritical point is obtained for the value of the bond concentration in a restricted region. We also observe that the reentrant phase transition may occur in the present system if single-ion anisotropy parameter is not large and if transverse field is small. On the other hand, for certain values of the system parameters, new induced magnetic ordering can be obtained. We find a number of interesting phenomena that are not predicted by previous literatures. The influence of the transverse field on the behaviours of the reentrant phase transition and induced magnetic ordering is discussed. A detailed description of the phase transition is presented.
We investigate the phase transitions and tricritical behaviors of the frustrated Ising antiferromagnet with first- (J_{1}<0) and second- (J_{2}<0) nearest-neighbor interactions in a transverse field Ω on the square lattice using an effective-field theory with correlations based on a single-spin approximation. We have proposed a functional for the free energy to obtain the phase diagram in the T-R (R=J_{2}/|J_{1}|) or T-Ω planes. It is shown that due to the transverse field the phase transition between ordered and disordered phases changes in the tricritical point (TCP) from the second order to the first order. The longitudinal and transverse magnetizations are also studied for selected values of R and Ω. In particular, the variation of TCP at the ground state in the three-dimensional space is constructed. For some special cases, values of the critical temperature and the critical transverse field have been determined analytically.
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.