University of Kentucky

Abstract: Deconfinement in the Two Dimensional XY Model

The classical XY ferromagnet in two dimensions is well-known to support a phase transition, in spite of the absence of spontaneous long-range order in such low dimension. This occurs through the proliferation of vortices at some critical temperature. What happens to this transition when an ordering, in-plane magnetic field is applied? In addition to vortices, the system now supports topological defects in the form of strings. These run between vortex-antivortex pairs and introduce a linear confining potential. According to conventional wisdom, this should suppress the unbinding transition. We revisit this old problem, and argue that in fact vortex deconfinement can occur in this system, via a two-step process: with increasing fluctuations, strings first proliferate through the system, and then vortices unbind. The transitions turn out to be remarkably continuous, and indeed challenge standard ideas about what consitutes a phase transition. Results of simulations supporting the existence of a continuous unbinding transition will be presented. Possible applications, including to bilayer quantum Hall and superconducting systems, unlocking of layered crystals, and Luttinger liquids, will be reviewed.