Comment on ``Hausdorff Dimension of Critical Fluctuations in Abelian Gauge Theories"

Abstract

Hove, Mo, and Sudbo [Phys. Rev. Lett. 85, 2368 (2000)] derived a simple connection, $η+ D_H = 2$, between the anomalous scaling dimension $η$ of the U(1) universality class order parameter and the Hausdorff dimension $D_H$ of critical loops in loop representations of U(1) models. We show that the above relation is wrong and establish a correct relation that contains a new critical exponent.