Helium in Vycor, constrained randomness, and the Harris criterion

Standard arguments for the relevance or otherwise of random disorder at bulk criticality are reconsidered in relation to the crossover seen in the superfluid transition at low coverages of helium adsorbed in Vycor, a porous glass. It is argued that Vycor should be modeled by constrained randomness characterized by pair correlations vanishing with wave vector, q, as ‖q${\Vert }^{\mathrm{theta}}$, with, physically, theta=2. Simple scaling and Harris arguments yield a randomness crossover exponent ${\phi }_R$=α-thetaν (α and ν being the specific-heat and correlation-length exponents) but must be corrected, in the light of previous renormalization-group arguments, by taking proper account of nonlinear scaling fields or quadratic terms in the variation of transition temperature with disorder. In fact, constrained randomness is still relevant for α positive (as at a Gaussian fixed point describing ideal Bose behavior in dimensions d${\phi }_R$=1/2α. The interpretation of the experiments as indicative of crossover to ideal Bose criticality is discussed in the light of the results.