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Methods to determine the Hausdorff dimension of vortex loops in the three-dimensional XY model

M. Camarda·F. Siringo·R. Pucci·A. Sudbo·J. Hove
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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.

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M. Camarda, F. Siringo, R. Pucci, A. Sudbo, J. Hove. 2006-07-31. Methods to determine the Hausdorff dimension of vortex loops in the three-dimensional XY model. https://doi.org/10.1103/physrevb.74.104507

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