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 D_H of the vortex loops which are the critical fluctuations of the 3D XY model. We also present analytical arguments for why \vartheta in the scaling relation η_ϕ + D_H = 2 + \vartheta between D_H and the anomalous scaling dimension of the corresponding field theory, must be zero.

arXiv commentTo appear in Phys. Rev. B

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• Berezinskii-Kosterlitz-Thouless and Vogel-Fulcher-Tammann criticality in $\mathrm{XY}$ model
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