  Field-induced magnetic ordering in the structurally disordered quantum
magnets Ni(Cl$_{1-x}$Br$_x$)$_2$$\cdot$4SC(NH$_2$)$_2$, $x=8$% and 13%, is
studied by means of neutron diffraction. The order parameter critical exponent
is found to be very close to its value $\beta=0.5$ expected for magnetic
Bose-Einstein condensation in the absence of disorder. This result applies to
temperatures down to 40 mK, and a 1 T range in magnetic field. The crossover
exponent is found to be $\phi \sim 0.4$, for temperature ranges as small as 300
mK. Possible reasons for a discrepancy with recent numerical simulations and
bulk measurements are discussed.
