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Chinese Physics Letters

Quantum XY Spin Glass Model with Longitudinal Ferromagnetic Coupling

Shang Yu-Min, K.L. Yao

Published May 1, 1999• 1 citation
Publisher

Abstract

The quantum XY spin glass model with longitudinal ferromagnetic coupling is investigated in static replica symmetry limit. Several thermodynamic quantities are calculated numerically. We find that the ferromagnetic coupling enhances the stability of replica symmetric solution. A 2-dimensional Ising model like transition is found, which demonstrates that the ferromagnetic coupling increases the order of spin glass model. Affected by the ferromagnetic coupling, transverse component of the susceptibility has two cusps corresponding to transverse-longitudinal spin-glass phase transition and longitudinal spin glass-paramagnetic transition separately.

DOI
10.1088/0256-307x/16/5/024

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In the replica symmetric approximation and the static limit in Matsubara ``imaginary time,'' we have investigated a quantum XY spin-glass system with the ferromagnetic coupling and the uniaxial anisotropy numerically. We found that, for S=1,S=1,S=1, under the uniaxial anisotropy, the spin-glass phase breaks into two phases: a longitudinal spin-glass phase, and a spin-glass phase; the mixed phase of the spin glass and the ferromagnet breaks into two phases: a mixed phase of the longitudinal spin glass and the longitudinal ferromagnet, a mixed phase of the spin glass and the ferromagnet; the peak in the curve of the specific heat versus temperature is split into two peaks: the peak of uniaxial anisotropy and the peak of the ferromagnetic coupling. The system will be dominated by the random exchange interaction if the probability of the random exchange interaction taking negative value is greater than 15.87%. In the absence of the uniaxial anisotropy, there is a mean-interaction translational invariance in the spin-glass phase and the paramagnetic phase. In the presence of the uniaxial anisotropy, there is a mean-interaction translational invariance in the spin-glass phase, the longitudinal spin-glass phase and the paramagnetic phase. In these phases, the entropy, the specific heat and the susceptibility do not depend on the mean-interaction.
The van Hemmen model with a transverse field is studied to describe the quantum Ising spin glass. The free energy and phase diagrams (T(T(T versus $\ensuremath{\Omega},$ and T versus Jo/J,{J}_{o}/J,Jo​/J, where $\ensuremath{\Omega}$ is the transverse field, Jo{J}_{o}Jo​ and J are the ferromagnetic and random exchange interactions, respectively) are calculated for the model with two-peaked and Gaussian exchange distribution. The system presents three ordered phases, namely, spin glass, mixed, and ferromagnetic phases, besides the paramagnetic disordered phase. The influence of the transverse field $\ensuremath{\Omega}$ is to destroy the ordered phases. In the $(T,\ensuremath{\Omega})$ plane our results are compared with those obtained by the replica-symmetry-breaking solution and the same qualitative behavior is observed for the spin-glass transition.