Nonperturbative Approach to Correlations in Two-Dimensional Vortex Liquids

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 nonperturbative 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 order diverges only in the zero-temperature limit, which indicates the absence of a finite-temperature phase transition to the vortex lattice phase.