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We calculate the renormalized quartic vertex function of the Ginzburg-Landaumodel for a superconducting film in a magnetic field by summing an infinitesubset of diagrams, the so-called parquet graphs. Using this non-perturbativesolution, 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 crystallineorderdiverges only in the zero-temperature limit, which indicates the absenceof a finite temperature phase transition to the vortex lattice phase.Comment: 4 pages, Revtex+epsf, 3 figures are included as a uuencoded .eps fil

Nonperturbative Approach to Correlations in Two-Dimensional Vortex Liquids