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

TL;DR

This paper investigates a 3D lattice loop model with 1/r^2 interactions, revealing a continuous line of second-order phase transitions with varying critical properties, including an exactly solvable critical point.

Contribution

It introduces a 3D loop model with 1/r^2 interactions and characterizes its phase diagram, including an exactly self-dual point with a calculable critical conductivity.

Findings

Identifies a line of second-order phase transitions with varying exponents.

Determines the critical conductivity exactly at the self-dual point.

Shows the correlation length exponent varies along the transition line.

Abstract

We study a lattice model of interacting loops in three dimensions with a $1/r^2$ interaction. Using Monte Carlo, we find 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.