Phase Transitions in the Two-Dimensional Random Gauge XY Model

TL;DR

This study uses Monte Carlo simulations to explore the phase diagram of the 2D random gauge XY model, revealing persistent superconductivity at low temperatures across all disorder levels and identifying different transition types.

Contribution

It demonstrates that the 2D random gauge XY model remains superconducting at low temperatures regardless of disorder strength, contrasting earlier conclusions, and distinguishes transition types at different disorder levels.

Findings

Superconductivity persists at low T for all disorder strengths.

Transition types differ: KT at weak disorder, non-KT at strong disorder.

Contradicts previous studies suggesting disorder destroys superconductivity.

Abstract

The two-dimensional random gauge \xy model, where the quenched random variables are magnetic bond angles uniformly distributed within $[-r\pi, r\pi]$ ($0 \leq r \leq 1$), is studied via Monte Carlo simulations. We investigate the phase diagram in the plane of the temperature $T$ and the disorder strength $r$, and infer, in contrast to a prevailing conclusion in many earlier studies, that the system is superconducting at any disorder strength $r$ for sufficiently low $T$. It is also argued that the superconducting to normal transition has different nature at weak disorder and strong disorder: termed Kosterlitz-Thouless (KT) type and non-KT type, respectively. The results are compared to earlier works.