  We report ac susceptibility, specific heat, and neutron scattering
measurements on a dipolar-coupled antiferromagnet LiYbF$_4$. For the thermal
transition, the order-parameter critical exponent is found to be 0.20(1) and
the specific-heat critical exponent -0.25(1). The exponents agree with the 2D
XY/h$_4$ universality class despite the lack of apparent two-dimensionality in
the structure. The order-parameter exponent for the quantum phase transitions
is found to be 0.35(1) corresponding to (2+1)D. These results are in line with
those found for LiErF$_4$ which has the same crystal structure, but largely
different T$_N$, crystal field environment and hyperfine interactions. Our
results therefore experimentally establish that the dimensional reduction is
universal to quantum dipolar antiferromagnets on a distorted diamond lattice.
