Methods to determine the Hausdorff dimension of vortex loops in the three-dimensional XY model
arXiv:cond-mat/0607830 · doi:10.1103/PhysRevB.74.104507
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.
To appear in Phys. Rev. B