Superfluid transition of 4He in ultralight aerogel

We present superfluid density and heat capacity results of 4He entrained in 5%, 2%, and 0.5% dense silica aerogel. The superfluid density exponent shows a systematic decrease towards the bulk 4He value with decreasing aerogel density. Singular contribution to heat capacity is observed on both sides of the transition in aerogel of 2% and 0.5% silica. In the lightest sample, the scaling law α=α and the hyperscaling relation 2-α=dν=dζ are satisfied.