  We consider the quantum magnet $\rm LiHo_xY_{1-x}F_4$ at $x = 0.167$.
Experimentally the spin glass to paramagnet transition in this system was
studied as a function of the transverse magnetic field and temperature, showing
peculiar features: for example (i) the spin glass order is destroyed much
faster by thermal fluctuations than by the transverse field; and (ii) the cusp
in the nonlinear susceptibility signaling the glass state {\it decreases} in
size at lower temperature. Here we show that the hyperfine interactions of the
Ho atom must dominate in this system, and that along with the transverse
inter-Ho dipolar interactions they dictate the structure of the phase diagram.
The experimental observations are shown to be natural consequences of this.
