  The LiHo$_x$Y$_{1-x}$F$_4$ magnetic material in a transverse magnetic field
$B_{x}\hat x$ perpendicular to the Ising spin direction has long been used to
study tunable quantum phase transitions in a random disordered system. We show
that the $B_{x}-$induced magnetization along the $\hat x$ direction, combined
with the local random dilution-induced destruction of crystalline symmetries,
generates, via the predominant dipolar interactions between Ho$^{3+}$ ions,
{\it random fields} along the Ising $\hat z$ direction. This identifies
LiHo$_x$Y$_{1-x}$F$_4$ in $B_x$ as a new random field Ising system. The random
fields explain the rapid decrease of the critical temperature in the diluted
ferromagnetic regime and the smearing of the nonlinear susceptibility at the
spin glass transition with increasing $B_{x}$, and render the $B_{x}-$induced
quantum criticality in LiHo$_x$Y$_{1-x}$F$_4$ likely inaccessible.
