  We have performed Monte Carlo studies of the 3D $XY$ model with random
uniaxial anisotropy, which is a model for randomly pinned spin-density waves.
We study $L \times L \times L$ simple cubic lattices, using $L$ values in the
range 16 to 64, and with random anisotropy strengths of $D / 2 J$ = 1, 2, 3, 6
and $\infty$. There is a well-defined finite temperature critical point, $T_c$,
for each these values of $D / 2 J$. We present results for the angle-averaged
magnetic structure factor, $S (k)$ at $T_c$ for $L = 64$. We also use
finite-size scaling analysis to study scaling functions for the critical
behavior of the specific heat, the magnetization and the longitudinal magnetic
susceptibility. Good data collapse of the scaling functions over a wide range
of $T$ is seen for $D / 2 J$ = 6 and $\infty$. For our finite values of $D / 2
J$ the scaled magnetization function increases with $L$ below $T_c$, and
appears to approach an $L$-independent limit for large $L$. This suggests that
the system is ferromagnetic below $T_c$.
