Quenched disorder and spin-glass correlations in XY nematics

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 Q and the effective disorder strength Gamma. These results, xi similar to Q(2) e(1/Q2) and xi similar to (1/Gamma) e(-Gamma), clarify what happens in the limiting cases of diminishing Q and Gamma, that is near a phase transition of a pure system. In particular, it is found that quenched disorder is irrelevant as Q -> 0 and hence does not change the character of the continuous XY nematic-isotropic phase transition. We discuss how these results compare with experiments and simulations.