Possible first order transition in the two-dimensional Ginzburg-Landau model induced by thermally fluctuating vortex cores

TL;DR

This paper investigates how including thermal amplitude fluctuations in the 2D Ginzburg-Landau model affects the vortex unbinding transition, suggesting it may be a first order transition instead of the traditional Kosterlitz-Thouless transition.

Contribution

It introduces a systematic way to incorporate amplitude fluctuations into the vortex gas description, challenging the conventional understanding of the transition nature.

Findings

Vortices form a Coulomb gas with increased fugacity due to amplitude fluctuations.

The transition may be first order if the correlation length is sufficiently large.

Results align with Minnhagen's phase diagram of the 2D Coulomb gas.

Abstract

We study the two-dimensional Ginzburg-Landau model of a neutral superfluid in the vicinity of the vortex unbinding transition. The model is mapped onto an effective interacting vortex gas by a systematic perturbative elimination of all fluctuating degrees of freedom (amplitude {\em and} phase of the order parameter field) except the vortex positions. In the Coulomb gas descriptions derived previously in the literature, thermal amplitude fluctuations were neglected altogether. We argue that, if one includes the latter, the vortices still form a two- dimensional Coulomb gas, but the vortex fugacity can be substantially raised. Under the assumption that Minnhagen's generic phase diagram of the two- dimensional Coulomb gas is correct, our results then point to a first order transition rather than a Kosterlitz-Thouless transition, provided the Ginzburg-Landau correlation length is large enough in units of a microscopic cutoff length for fluctuations. The experimental relevance of these results is briefly discussed. [Submitted to J. Stat. Phys.]