Line of continuous phase transitions in a three dimensional U(1) 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, 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.

6 pages, 6 figures

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• Duality and Universal Transport in a Mixed-Dimension Electrodynamics
• Loop Models, Modular Invariance, and Three Dimensional Bosonization
• Higher-form Symmetries under Weak Measurement
• Phases and phase transitions in a $U(1)\times U(1)$ system with $\theta =2\pi /3$ mutual statistics
• Monte Carlo Study of a $U(1)\times U(1)$ Loop Model with Modular Invariance
• Quantization of a Self-dual Conformal Theory in (2+1) Dimensions
• Self-dual criticality in three-dimensional ${\mathbb{Z}}_2$ gauge theory with matter