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Communications in Theoretical Physics

Quantum SK S = 1 Spin Glass with Uniaxial Interactions

Yiqin Xiong, Yue Shang, Lin Yi, K.L. Yao

Published Jun 15, 1996• 0 citations
Publisher

Abstract

The quantum Sherrington-Kirkpatrick (SK) S = 1 spin-glass model with uniaxial anisotropy in applied magnetic field is investigated numerically. The dependences of entropy, specific heat and susceptibility on temperature are calculated for different magnetic fields. The dependence of specific heat on temperature exhibits the typical spin-glass characteristics. It is found that the susceptibility depends strongly on the sign of uniaxial anisotropy constants.

DOI
10.1088/0253-6102/25/4/397

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The quantum Sherrington-Kirkpatrick (SK) S = 1 spin-glass model with uniaxial anisotropy in applied magnetic field is investigated numerically. The dependences of entropy, specific heat and susceptibility on temperature are calculated for different magnetic fields. The dependence of specific heat on temperature exhibits the typical spin-glass characteristics. It is found that the susceptibility depends strongly on the sign of uniaxial anisotropy constants.
In the static replica symmetric approximation, a quantum Heisenberg S=1 spin-glass model with single-ion uniaxial anisotropy and infinite-range random Dzyaloshinskii-Moriya (DM) interaction in applied magnetic fields is investigated. The local susceptibility and the corresponding order parameters are calculated numerically, and are found to be in good agreement with those of thermofield dynamics. The dependences of entropy and specific heat on temperature are studied numerically at various magnetic fields. It is shown that the entropy is always positive and the quantum fluctuation has a very strong effect on the specific heat. Especially, the typical crossover behaviour of the specific heat of a spin glass at various magnetic fields for mixed-anisotropy interactions is found.
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.
I study in detail the quantum Sherrington-Kirkpatrick (SK) model, i.e., the infinite-range Ising spin glass in a transverse field, by solving numerically the effective one-dimensional model that the quantum SK model can be mapped to in the thermodynamic limit. I find that the replica symmetric solution is unstable down to zero temperature, in contrast to some previous claims, and so there is not only a line of transitions in the (longitudinal) field-temperature plane (the de Almeida-Thouless, AT, line) where replica symmetry is broken, but also a quantum de Almeida-Thouless (QuAT) line in the transverse field-longitudinal field plane at T=0. If the QuAT line also occurs in models with short-range interactions its presence might affect the performance of quantum annealers when solving spin glass-type problems with a bias (i.e., magnetic field).
We study a quantum generalization of the infinite-range Sherrington-Kirkpatrick spin-glass model with biaxial crystal-field effects described by two uniaxial anisotropy parameters D x and D y . For spin dimensionality S = 1 we report an analytical and numerical analysis in the ( T , D x , D y ) parameter space (with T being the temperature). For D ≡ D x = D y the model effectively becomes classical and identical with the crystal-field-split spin-glass Ising model (introduced by Ghatak and Sherrington) showing a discontinuous phase transition to the spin-glass phase on a portion of the T - D line.