New universality class for the three-dimensional XY model with correlated impurities: Application to ⁴He in aerogels

Encouraged by experiments on $^4$He in aerogels, we confine planar spins in the pores of simulated aerogels (diffusion limited cluster-cluster aggregation) in order to study the effect of quenched disorder on the critical behavior of the three-dimensional XY model. Monte Carlo simulations and finite-size scaling are used to determine critical couplings $K_c$ and exponents. In agreement with experiments, clear evidence of change in the thermal critical exponents $\nu$ and $\alpha$ is found at nonzero volume fractions of impurities. These changes are explained in terms of {\it hidden} long-range correlations within disorder distributions.