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 (Formula presented) for the order-disorder phase transition at T=0, the average nonlinear susceptibility (Formula presented) diverges in the paramagnetic phase for Γ well above (Formula presented), as is also demonstrated in the accompanying paper by Rieger and Young. In d=3, the linear susceptibility remains finite at (Formula presented), and while Griffiths singularity effects are certainly observable in the paramagnetic phase, the nonlinear susceptibility appears to diverge only rather close to (Formula presented). These results show that Griffiths singularities remain persistent in dimensions above one (where they are known to be strong), though their magnitude decreases monotonically with increasing dimensionality (there being no Griffiths singularities in the limit of infinite dimensionality).