Abstract
The superfluid density of liquid4He is computed from vortex renormalization theories for the case of a slab geometry with a slab height L. With increasing temperature there is a crossover from three dimensions to two as the size of the largest vortex rings approaches L and they intersect with the walls, forming vortex pairs. The superfluid density becomes anisotropic, with the component parallel to the slab undergoing the universal Kosterlitz-Thouless jump, while the perpendicular component remains finite. The results are in agreement with both finite-size scaling and Monte-Carlo simulations.
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