Critical Behavior of Superfluid4He in Aerogel

We report Monte Carlo studies of the critical behavior of superfluid ${}^4$He in the presence of quenched disorder with long-range fractal correlations. Modeling aerogel as an incipient percolating cluster in 3D and weakening the bonds at the fractal sites, XY-model simulations demonstrate an increase in the superfluid density exponent $\zeta$ from $0.67\pm 0.005$ for the pure case to an apparent value of $0.722\pm 0.005$ in the presence of the fractal disorder, provided that the helium correlation length does not exceed the fractal correlation length.