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

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

2006-07-31

arxiv.org/abs/cond-mat/0607830v1

Phys. Rev. B 74, 104507 (2006)

Physics

Condensed Matter

Superconductivity

To appear in Phys. Rev. B

Scientific paper

10.1103/PhysRevB.74.104507

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 \eta_{\phi} + D_H = 2 + \vartheta between D_H and the anomalous scaling dimension of the corresponding field theory, must be zero.

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