We study the three-dimensional quantum Ising spin glass in a transverse magnetic field following the evolution of the bond probability distribution under renormalization-group transformations. The phase diagram (critical temperature ${\mathit{T}}_{\mathit{c}}$ vs transverse field Γ) we obtain shows a finite slope near T=0, in contrast with the infinite slope for the pure case. Our results compare very well with the experimental data recently obtained for the dipolar Ising spin glass ${\mathrm{LiHo}}_{0.167}$${\mathrm{Y}}_{0.833}$${\mathrm{F}}_4$, in a transverse field. This indicates that this system is more appropriately described by a model with short-range interactions than by an equivalent Sherrington-Kirkpatrick model in a transverse field.

• Received 24 November 1993

DOI:https://doi.org/10.1103/PhysRevB.49.6404