  We consider the isotropic-to-nematic transition in liquid crystals confined
to aerogel hosts, and assume that the aerogel acts as a random field. We
generally find that self-averaging is violated. For a bulk transition that is
weakly first-order, the violation of self-averaging is so severe, even the
correlation length becomes non-self-averaging: no phase transition remains in
this case. For a bulk transition that is more strongly first-order, the
violation of self-averaging is milder, and a phase transition is observed.
