Non-perturbative approach to correlations in two-dimensional vortex liquids

TL;DR

This paper develops a non-perturbative method to analyze correlations in 2D vortex liquids, revealing the absence of a finite-temperature vortex lattice transition and showing increasing crystalline order as temperature decreases.

Contribution

It introduces a non-perturbative calculation of the vortex liquid structure factor using parquet graphs, providing new insights into vortex ordering without a phase transition.

Findings

Crystalline order grows as temperature decreases

No finite-temperature phase transition to vortex lattice

Diverging length scale only at zero temperature

Abstract

We calculate the renormalized quartic vertex function of the Ginzburg-Landau model for a superconducting film in a magnetic field by summing an infinite subset of diagrams, the so-called parquet graphs. Using this non-perturbative solution, we obtain the structure factor of the two-dimensional vortex liquid. We find growing crystalline order in the system as the temperature is lowered. Our results suggest that the length scale characterizing the crystalline orderdiverges only in the zero-temperature limit, which indicates the absence of a finite temperature phase transition to the vortex lattice phase.