The geometric properties of critical fluctuations in the three-dimensional (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 Theta in the scaling relation eta(phi)+D-H=2+Theta between D-H and the anomalous scaling dimension of the corresponding field theory must be zero.
Methods to determine the Hausdorff dimension of vortex loops in the three-dimensional XY model
SIRINGO, Fabio;
2006-01-01
Abstract
The geometric properties of critical fluctuations in the three-dimensional (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 Theta in the scaling relation eta(phi)+D-H=2+Theta between D-H and the anomalous scaling dimension of the corresponding field theory must be zero.File in questo prodotto:
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