  Hove, Mo, and Sudbo [Phys. Rev. Lett. 85, 2368 (2000)] derived a simple
connection, $\eta + D_H = 2$, between the anomalous scaling dimension $\eta$ 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.
