Quantum vector spin glasses with random Dzyaloshinsky-Moriya interactions

Abstract

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.