Quantum and Classical Glass Transitions in $Li Ho_x Y_{1-x} F_4$

When performed in the proper low field, low frequency limits, measurements of the dynamics and the nonlinear susceptibility in the model Ising magnet in transverse field, $text{LiHo}_xtext{Y}_{1-x}text{F}_4$, prove the existence of a spin glass transition for $x$ = 0.167 and 0.198. The classical behavior tracks for the two concentrations, but the behavior in the quantum regime at large transverse fields differs because of the competing effects of quantum entanglement and random fields.