The uniformly frustrated two-dimensional XY model in the limit of weak frustration

TL;DR

This paper studies how a small uniform magnetic field affects the critical behavior of the 2D XY model, showing that even weak frustration destroys the phase transition and leads to paramagnetism at all temperatures.

Contribution

It demonstrates that weak uniform frustration destabilizes the XY model's critical line, providing theoretical predictions confirmed by numerical simulations.

Findings

Uniform frustration destroys the critical line of the XY model.

Correlation length diverges differently as frustration approaches zero.

Magnetic susceptibilities behave predictably with decreasing frustration.

Abstract

We consider the two-dimensional uniformly frustrated XY model in the limit of small frustration, which is equivalent to an XY system, for instance a Josephson junction array, in a weak uniform magnetic field applied along a direction orthogonal to the lattice. We show that the uniform frustration (equivalently, the magnetic field) destabilizes the line of fixed points which characterize the critical behaviour of the XY model for T <= T_{KT}, where T_{KT} is the Kosterlitz-Thouless transition temperature: the system is paramagnetic at any temperature for sufficiently small frustration. We predict the critical behaviour of the correlation length and of gauge-invariant magnetic susceptibilities as the frustration goes to zero. These predictions are fully confirmed by the numerical simulations.