Quantum Griffiths singularities in the transverse-field Ising spin glass.

We report a Monte Carlo study of the effects of fluctuations in the bond distribution of Ising spin glasses in a transverse magnetic field, in the paramagnetic phase in the T → 0 limit. Rare, strong fluctuations give rise to Griffiths singularities, which can dominate the zero-temperature behavior of these quantum systems, as originally demonstrated by McCoy for one-dimensional (d = 1) systems. Our simulations are done on a square lattice in d = 2 and a cubic lattice in d = 3, for a gaussian distribution of nearest neighbor (only) bonds. In d = 2, where the linear susceptibility was found to diverge at the critical transverse field strength Γc for the order-disorder phase transition at T = 0, the average nonlinear susceptibility χnl diverges in the paramagnetic phase for Γ well above Γc, as is also demonstrated in the accompanying paper by