Topological phase-fluctuations, amplitude fluctuations, and criticality in extreme type-II superconductors

We study the effect of critical fluctuations on the $(B,T)$ phase diagram in extreme type-II superconductors in zero and finite magnetic field using large-scale Monte Carlo simulations on the Ginzburg-Landau model in a frozen gauge approximation. We show that a vortex-loop unbinding gives a correct picture of the zero field superconducting-normal transition even in the presence of amplitude fluctuations, which are far from being critical at $T_c$. We extract critical exponents of the dual model by studying the topological excitations of the original model. From the vortex-loop distribution function we extract the anomalous dimension of the dual field $\eta \simeq -0.18$, and conclude that the charged Ginzburg-Landau model and the neutral 3DXY model belong to different universality classes. We find are two distinct scaling regimes for the vortex-line lattice melting line: a high-field scaling regime and a distinct low-field 3DXY critical scaling regime. We also find indications of an abrupt change in the connectivity of the vortex-tangle in the vortex liquid along a line $T_L \geq T_M$. This is the finite field counter-part of the zero-field vortex-loop blowout. Which at low enough fields appears to coincide with $T_M$. Here, a description of the vortex system only in terms of field induced vortex lines is inadequate at and above the VLL melting temperature.