Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. B, Condensed matter

Quantum Heisenberg spin glasses: Anisotropy effects and field dependence

T. K. Kopeć, G. Büttner, Klaus D. Usadel

Published May 1, 1990• 25 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.41.9221

Related papers

Competition between axial and cubic anisotropies in Heisenberg spin glasses

Zbigniew Domański

An infinite-range quantum Heisenberg spin glass with uniaxial (D) and cubic (K) anisotropies is studied using the thermo-field-dynamic method. Mean-field theory phase diagrams in the temperature-anisotropy plane (T,D) for quantum spins S=2 and S=5/2 are presented for different values of K. Generally, for integer spin values and large anisotropy D a condensation into a nonmagnetic spin state occurs, accompanied by the destruction of the spin-glass order as indicated by the finite critical value ${\mathrm{D}}_{\mathrm{c}}$(T=0). For half-integer S and sufficiently low temperature, the spin-glass phase persists for arbitrary D and K. In both cases the presence of a cubic term induces complicated crossovers from longitudinal to transverse freezing of spins.

Physical review. B, Condensed matter•Mar 1, 1997•1 citation

Field-induced crossover behavior in quantum Heisenberg spin glasses with random-anisotropy axes

T. K. Kopeć, G. Büttner

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.

Physical review. B, Condensed matter•Mar 1, 1992•2 citations

Quantum vector spin glasses with random Dzyaloshinsky-Moriya interactions

T. K. Kopeć, G. Büttner

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 [${\mathit{T}}_{\mathit{c}}$(h)\ensuremath{\propto}${\mathit{h}}^{2/3}$] for small fields to the Gabay-Toulouse (GT) -like behavior [${\mathit{T}}_{\mathit{c}}$(h)\ensuremath{\propto}${\mathit{h}}^{2}$] 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.

Physical review. B, Condensed matter•May 1, 1991•13 citations

Quantum spin glasses with cubic anisotropy

Z. Doman´ski, T. K. Kopeć, F. Pa´zma´ndi

An infinite-range quantum Ising spin glass with cubic anisotropy (K) is studied using the imaginary-time representation with the n-replica approach and the thermofield dynamic method. Mean-field-theory phase diagrams in the temperature-anisotropy plane (T,K) for quantum spins S ranging from 2 to 9/2 are presented. For integer-spin values and large cubic anisotropy (positive or negative, depending on S) a condensation into a nonmagnetic spin state occurs, accompanied by the destruction of the spin-glass order as indicated by the finite critical value ${\mathit{K}}_{\mathit{c}}$(T=0). For half-integer S and sufficiently low temperature the spin-glass phase persists for arbitrary K.

Physical review. B, Condensed matter•Feb 1, 1994•2 citations

Instabilities in the quantum Sherrington-Kirkpatrick Ising spin glass in transverse and longitudinal fields

T. K. Kopeć, Klaus D. Usadel, G. Büttner

The infinite-range quantum Ising spin glass in transverse ($\ensuremath{\Gamma}$) and longitudinal ($h$) fields is studied by means of thermo-field-dynamics as a substitute for the $n$-replica trick. With the use of a one-loop approximation for the dynamic self-interaction the stability of the mean-field-type solution against the action of fluctuations is investigated in the parameter space (${k}_{B}T, \ensuremath{\Gamma}, h$).

Physical review. B, Condensed matter•Jun 1, 1989•45 citations

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

Yiqin Xiong, Yue Shang, Lin Yi +1 more

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.

Journal of Physics Condensed Matter•Apr 3, 1995•1 citation
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.
An infinite-range quantum Heisenberg spin glass with uniaxial (D) and cubic (K) anisotropies is studied using the thermo-field-dynamic method. Mean-field theory phase diagrams in the temperature-anisotropy plane (T,D) for quantum spins S=2 and S=5/2 are presented for different values of K. Generally, for integer spin values and large anisotropy D a condensation into a nonmagnetic spin state occurs, accompanied by the destruction of the spin-glass order as indicated by the finite critical value Dc{\mathrm{D}}_{\mathrm{c}}Dc​(T=0). For half-integer S and sufficiently low temperature, the spin-glass phase persists for arbitrary D and K. In both cases the presence of a cubic term induces complicated crossovers from longitudinal to transverse freezing of spins.
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 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.
An infinite-range quantum Ising spin glass with cubic anisotropy (K) is studied using the imaginary-time representation with the n-replica approach and the thermofield dynamic method. Mean-field-theory phase diagrams in the temperature-anisotropy plane (T,K) for quantum spins S ranging from 2 to 9/2 are presented. For integer-spin values and large cubic anisotropy (positive or negative, depending on S) a condensation into a nonmagnetic spin state occurs, accompanied by the destruction of the spin-glass order as indicated by the finite critical value Kc{\mathit{K}}_{\mathit{c}}Kc​(T=0). For half-integer S and sufficiently low temperature the spin-glass phase persists for arbitrary K.
The infinite-range quantum Ising spin glass in transverse ($\ensuremath{\Gamma}$) and longitudinal (hhh) fields is studied by means of thermo-field-dynamics as a substitute for the nnn-replica trick. With the use of a one-loop approximation for the dynamic self-interaction the stability of the mean-field-type solution against the action of fluctuations is investigated in the parameter space (${k}_{B}T, \ensuremath{\Gamma}, h$).
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.