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 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 matterMar 1, 19922 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.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 matterMay 1, 199113 citations

Numerical simulations of spin glasses

I. Morgenstern

Lecture notes in physicsJan 1, 19836 citations

{\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.