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.
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