Vortex Deconfinement in the XY Model with a Magnetic Field

TL;DR

This paper investigates vortex unbinding in the 2D XY model under a magnetic field, revealing a two-step unbinding process with continuous transitions that differ from the classic Kosterlitz-Thouless transition.

Contribution

It introduces a combined renormalization group and duality analysis to describe vortex unbinding in the XY model with a magnetic field, highlighting lattice-dependent properties.

Findings

Vortex unbinding occurs via a two-step process involving spin string proliferation.

Transitions are continuous but not of the Kosterlitz-Thouless type.

Unbound vortex fixed point reflects lattice symmetry through nodal lines.

Abstract

We study vortex unbinding for the classical two-dimensional XY model in a magnetic field on square and triangular lattices. A renormalization group analysis combined with duality in the model shows that at high temperature and high field, the vortices unbind as the magnetic field is lowered in a two-step process: strings of overturned spins first proliferate and then vortices unbind. The transitions are highly continuous but are not of the Kosterlitz-Thouless type. The unbound vortex fixed point is shown to inherit properties of the underlying lattice, in particular containing a set of nodal lines that reflect the lattice symmetry.