Parquet Graph Resummation Method for Vortex Liquids

Abstract

We present in detail a nonperturbative method for vortex liquid systems. This method is based on the resummation of an infinite subset of Feynman diagrams, the so-called parquet graphs, contributing to the four-point vertex function of the Ginzburg-Landau model for a superconductor in a magnetic field. We derive a set of coupled integral equations, the parquet equations, governing the structure factor of the two-dimensional vortex liquid system with and without random impurities and the three-dimensional system in the absence of disorder. For the pure two-dimensional system, we simplify the parquet equations considerably and obtain one simple equation for the structure factor. In two dimensions, we solve the parquet equations numerically and find growing translational order characterized by a length scale $R_c$ as the temperature is lowered. The temperature dependence of $R_c$ is obtained in both pure and weakly disordered cases. The effect of disorder appears as a smooth decrease of $R_c$ as the strength of disorder increases.

15 pages, 12 PostScript figures, uses multicols.sty and epsf.sty

References in corpus (6)

• Elastic Theory of pinned flux lattices
• Two-Dimensional Vortex Lattice Melting
• Replica Symmetry Breaking Instability in the 2D XY model in a random field
• Absence of the Transition into Abrikosov Vortex State of Two-Dimensional Type-II Superconductor with Weak Pinning
• Critical Fluctuations and Disorder at the Vortex Liquid to Crystal Transition in Type-II Superconductors
• Non-perturbative approach to correlations in two-dimensional vortex liquids

Cited by in corpus (14)

• The Ginzburg-Landau Theory of Type II superconductors in magnetic field
• Extreme Type-II Superconductors in a Magnetic Field: A Theory of Critical Fluctuations
• Solving the Parquet Equations for the Hubbard Model beyond Weak Coupling
• Mixed phases in U(N) superconductivity
• Summing parquet diagrams using the functional renormalization group: X-ray problem revisited
• Summation of Parquet diagrams as an ab initio method in nuclear structure calculations
• First-Order Transition and Critical End-Point in Vortex Liquids in Layered Superconductors
• Is there a Phase Transition to the Flux Lattice State?
• Numerical Investigation of the Dynamics of a Thin Film Type II Superconductor with and without Disorder
• Flux-lattice melting in two-dimensional disordered superconductors
• An Improved Nonperturbative Method for Studying Two-dimensional Vortex Liquids
• Non-commutative field theory approach to two-dimensional vortex liquid system
• Vanishing of Resistivity upon Freezing of Vortex Liquid in Clean Superconductors
• On the nature of the phase transitions in two-dimensional type II superconductors