Superfluid transition ofHe4films adsorbed on multiply connected surfaces

A Kosterlitz-Thouless–like approach is used to describe the superfluid transition of thin ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ films adsorbed on multiply connected surfaces such as packed powders or other porous materials. The elementary topological defect mediating the transition is a string linking two vortices of opposite circulation. The long-range interaction between strings gives rise to a phase transition which has a critical exponent for the superfluid density of ν=0.64.