2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113520The 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. BSuperconductivitytext