An Improved Nonperturbative Method for Studying Two-dimensional Vortex   Liquids
  We show how a systematic improvement can be made on the nonperturbative parquet approximation method which was previously used to study the effect of thermal fluctuations in vortex liquids in high-temperature superconductors. This is achieved by including an infinite subset of Feynman diagrams contributing to the renormalized four-point vertex function of the Ginzburg-Landau model, which was omitted in the original approximation. We find that the growing crystalline order in the vortex liquid is more pronounced in the improved approximation. In particular, the second and third peaks in the liquid structure factor, which appeared as one peak in the original approximation, are now resolved. 
J. Yeo, H. Park and S. Yi