Nonlinear Response in strongly diluted $LiH_x Y_{1-x} F$

$LiH_x Y_{1-x} F$ is a physical manifestation of the Ising model in transverse field, where substitution of Ho ions with magnetically inert Y generates random, internal transverse fields at the spin sites. In the low-temperature, small x regime, the spatial anisotropy of the dipolar interaction, disorder, and the random fields compete to balance tendencies towards glassy and spin liquid behavior and emphasize the effects of the nonlinear response. By measuring the ac magnetic susceptibility of single crystals with x=0.045 in both internal and external transverse fields, we explore the nonlinear dynamics and the stability of the glassy state.