Quantum vector spin-glass models in an applied field

We use the static approximation to investigate the phase diagram of the infinite-ranged quantum Heisenberg spin glass (QHSG) in an external field, as well as the phase diagram of a two-component quantum spin glass (QXYSG) in a transverse or a longitudinal field. For the QHSG we find that, for strong field (H) and low temperature (T), the phase transition into the spin-glass phase characterized by nonzero transverse spin-glass ordering is given by ${\mathit{T}}_{\mathit{c}}$∼exp[-${\mathit{H}}^2$/(2${\mathit{J}}^2$ ${\mathit{S}}^2$)], as compared with ${\mathit{T}}_{\mathit{c}}$∼exp{-${\mathit{H}}^2$/[2${\mathit{J}}^2$S(S+1)]} for classical spins of magnitude √S(S+1) . In the case of QXYSG in a transverse field (Γ), the phase boundary terminates at Γ/J=2 for T=0.