  We carry out a detailed deuterium NMR study of local nematic ordering in
polydomain nematic elastomers. This system has a close analogy to the
random-anisotropy spin glass. We find that, in spite of the quadrupolar nematic
symmetry in 3-dimensions requiring a first-order transition, the order
parameter in the quenched ``nematic glass'' emerges via a continuous phase
transition. In addition, by a careful analysis of the NMR line shape, we deduce
that the local director fluctuations grow in a critical manner around the
transition point. This could be the experimental evidence for the Aizenman-Wehr
theorem about the quenched impurities changing the order of discontinuous
transition.
