Methods to determine the Hausdorff dimension of vortex loops in the three-dimensional XY model
Abstract
The geometric properties of critical fluctuations in the 3D XY model are analyzed. The 3D XY model is a lattice model describing superfluids. We present a direct evaluation of the Hausdorff dimension DH of the vortex loops which are the critical fluctuations of the 3D XY model. We also present analytical arguments for why in the scaling relation ηφ + DH = 2 + between DH and the anomalous scaling dimension of the corresponding field theory, must be zero.
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