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Journal of Physics Condensed Matter

Quantum Heisenberg spin-glass model with mixed-anisotropy interactions in applied magnetic fields

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

Published Apr 3, 1995• 1 citation
Publisher

Abstract

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.

DOI
10.1088/0953-8984/7/14/023

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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 generalized quantum replica symmetric approximation, a quantum XY spin-glass model with ferromagnetic coupling and planar Dzyaloshinski–Mariya (DM) interactions is investigated theoretically. Entropy and specific heat are calculated numerically as well as spin self-interactions and spin-glass order parameters for spin . It is found that the double-cusp of the specific heat, which corresponds to the collinear ferromagnetic and the paramagnetic ferromagnetic transitions respectively, coincides completely due to DM-anisotropy interactions. Additionally, the local susceptibility and the spontaneous magnetization are evaluated numerically.
The infinite-range quantum vector spin glass with random Dzyaloshinsky-Moriya anisotropy (with variances J and D for random bonds and anisotropy, respectively) and external magnetic field (h) is studied by means of the thermofield dynamics as a substitute for the replica method for the spin values S=1/2, 1, and 3/2. The temperature-anisotropy phase diagrams have been calculated numerically for arbitrary anisotropy and different values of the applied magnetic field h. The stability analysis of the mean-field-type solution against the action of fluctuations has been performed, leading to the upper and lower critical lines in the field-temperature plane. For small values of the reduced anisotropy variance d=D/J (0.1d0.3), we find a crossover of the upper critical line from the de Almeida--Thouless (AT) -type behavior [Tc{\mathit{T}}_{\mathit{c}}Tc​(h)\ensuremath{\propto}h2/3{\mathit{h}}^{2/3}h2/3] for small fields to the Gabay-Toulouse (GT) -like behavior [Tc{\mathit{T}}_{\mathit{c}}Tc​(h)\ensuremath{\propto}h2{\mathit{h}}^{2}h2] for large fields. For larger anisotropies (d\ensuremath{\ge}0.3) the upper critical line is essentially that of the AT type. Interestingly, the lower critical line, which persists for d0.5, exhibits the reverse type of behavior for the corresponding values of the anisotropy d. Additionally, we have analyzed transverse and longitudinal susceptibilities for different values of the field h. We found that a small amount of the anisotropy d stabilizes a plateau of the local susceptibilities in the spin-glass phase.
The infinite-range quantum Heisenberg spin-glass model with random-anisotropy axes and external magnetic field (h) is studied by means of the thermofield dynamics for the spin value S=1/2. The stability of the mean-field-type solution against the action of fluctuations has been evaluated in the presence of h leading to the upper and lower critical lines in the field-temperature (h-T) plane. For small values of the anisotropy variance we find a crossover of the upper critical line from the de Almeida--Thouless-type behavior for small fields to the Gabay-Toulouse-like behavior for large fields and a reversed type of behavior at the lower critical line for corresponding values of the random anisotropy---in close analogy to the recently analyzed quantum vector spin glass with random Dzyaloshinsky-Moriya interactions.
The infinite-range quantum Heisenberg spin glass with uniaxial anisotropy (D) and coaxial external magnetic field (h) is studied by means of the thermo-field-dynamics as a substitute for the n-replica trick. Within the mean-field theory a multiplicity of spin-glass phases has been found for the spin values S=1 and S=3/2, respectively, including: longitudinal, transverse, and mixed phases. The stability of the mean-field-type solution against the action of fluctuations has been investigated and the existence of a crossover from the longitudinal-to-transverse freezing is demonstrated explicitly in the temperature-field (T-h) phase diagram for various values of the constant D.