Monte Carlo Study of a U(1)xU(1) system with \pi-statistical Interaction

TL;DR

This paper investigates a two-species loop system with mutual π-statistics in 2+1 dimensions, revealing a complex phase diagram with first-order transitions and phases where loops either coexist or are mutually exclusive.

Contribution

It introduces a reformulation of the U(1)×U(1) model suitable for Monte Carlo study and maps out its phase diagram, including the identification of a self-dual line and associated phase transitions.

Findings

Identified phases with no loops, single-species loop proliferation, and coexistence of loops avoiding statistical interactions.

Discovered first-order phase transitions along the self-dual line.

Compared behavior with a related model lacking the even-strength loop phase.

Abstract

We study a $U(1)\times U(1)$ system with two species of loops with mutual $\pi$-statistics in (2+1) dimensions. We are able to reformulate the model in a way that can be studied by Monte Carlo and we determine the phase diagram. In addition to a phase with no loops, we find two phases with only one species of loop proliferated. The model has a self-dual line, a segment of which separates these two phases. Everywhere on the segment, we find the transition to be first-order, signifying that the two loop systems behave as immiscible fluids when they are both trying to condense. Moving further along the self-dual line, we find a phase where both loops proliferate, but they are only of even strength, and therefore avoid the statistical interactions. We study another model which does not have this phase, and also find first-order behavior on the self-dual segment.