Dynamical universality classes of the superconducting phase transition

TL;DR

This study investigates the dynamical critical behavior of the XY-model in vortex representation at finite temperatures, revealing different universality classes depending on magnetic field fluctuation regimes relevant to high-temperature superconductors.

Contribution

It provides the first detailed Monte Carlo analysis of the XY-model's dynamical universality classes in two limits, including the effects of magnetic screening and vortex dynamics.

Findings

Dynamical critical exponent z ≈ 1.5 without magnetic fluctuations.

Dynamical critical exponent z ≈ 2.7 with strong magnetic screening.

Comparison with phase representation models and discussion of disorder effects.

Abstract

We present a finite temperature Monte Carlo study of the XY-model in the vortex representation, and study its dynamical critical behavior in two limits. The first neglects magnetic field fluctuations, corresponding to the absence of screening, which should be a good approximation in high $T_c$ superconductors ($\kappa\to \infty$) except extremely close to the critical point. Here, from finite size scaling of the linear resistivity we find the dynamical critical exponent of the vortex motion to be $z\approx 1.5$. The second limit includes magnetic field fluctuations in the strong screening limit ($\kappa\to 0$) corresponding to the true asymptotic inverted XY critical regime, where we find the unexpectedly large value $z\approx 2.7$. We compare these results, obtained from dissipative dynamics in the vortex representation, with the universality class of the corresponding model in the phase representation with propagating (spin wave) modes. We also discuss the effect of disorder and the relevance of our results for experiments.