A topological viewpoint of the superfluid transition of 4He in acrogel

The superfluid density critical exponent, ζ (ρs ∝ (T - Tc)ζ), in aerogel has an anomalous value of roughly 0.8. Previous explanations of this anomaly have attributed this change to the correlated disorder of the aerogel substrate. The author proposes an alternative mechanism: vortex excitations on the aerogel strands. These topological excitations are modeled as an abelian gauge theory on a simple cubic lattice. Results from the Monte Carlo simulations of the model will be presented. In addition, the author will discuss the relevance of the model to understanding the transition in other substrates and in 3He -4He mixtures in aerogel