Line of continuous phase transitions in a three-dimensional U(1) loop model with 1/r^2 current-current interactions

Abstract

We study a lattice model of interacting loops in three dimensions with a 1/r^2 interaction. Using Monte Carlo methods, we have found that the phase diagram contains a line of second-order phase transitions between a phase where the loops are gapped and a phase where they proliferate. The correlation length exponent and critical conductivity vary continuously along this line. Our model is exactly self-dual at a special point on the critical line, which allows us to calculate the critical conductivity exactly at this point.