  We present a theoretical study of the equilibrium ordering in a 3D XY nematic
system with quenched random disorder. Within this model, treated with the
replica trick and Gaussian variational method, the correlation length is
obtained as a function of the local nematic order parameter and the effective
disorder strength. These results clarify what happens in the limiting cases of
diminishing order parameter and disorder strength, that is near a phase
transition of a pure system. In particular, it is found that quenched disorder
is irrelevant as the order parameter tends to zero and hence does not change
the character of the continuous XY nematic to isotropic phase transition. We
discuss how these results compare with experiments and simulations
