Critical Scaling Properties at the Superfluid Transition of ⁴He in Aerogel

We study the superfluid transition of ⁴He in aerogel by Monte Carlo simulations and finite size scaling analysis. Aerogel is a highly porous silica glass, which we model by a diffusion limited cluster aggregation model. The superfluid is modeled by a three dimensional XY model, with excluded bonds to sites on the aerogel cluster. We obtain the correlation length exponent ν=0.73±0.02, in reasonable agreement with experiments and with previous simulations. For the heat capacity exponent α, both experiments and previous simulations suggest deviations from the Josephson hyperscaling relation α=2-dν. In contrast, our Monte Carlo results support hyperscaling with α=-0.2±0.05. We suggest a reinterpretation of the experiments, which avoids scaling violations and is consistent with our simulation results.