Vortex dynamics for two-dimensional XY models

TL;DR

This paper investigates vortex dynamics in two-dimensional XY models with RSJ and TDGL dynamics, confirming the Minnhagen phenomenology and scaling predictions for the dynamical critical exponent and nonlinear IV exponent.

Contribution

It provides simulation evidence supporting the scaling prediction for the dynamical critical exponent and confirms the applicability of Minnhagen phenomenology to both RSJ and TDGL dynamics.

Findings

Vortex response matches Minnhagen phenomenology for both dynamics.

Dynamical critical exponent z follows the scaling prediction z=1/ε̃T^{CG}-2≥2.

Nonlinear IV exponent a equals z+1 in the low-temperature phase.

Abstract

Two-dimensional XY models with resistively shunted junction (RSJ) dynamics and time dependent Ginzburg-Landau (TDGL) dynamics are simulated and it is verified that the vortex response is well described by the Minnhagen phenomenology for both types of dynamics. Evidence is presented supporting that the dynamical critical exponent $z$ in the low-temperature phase is given by the scaling prediction (expressed in terms of the Coulomb gas temperature $T^{CG}$ and the vortex renormalization given by the dielectric constant $\tilde\epsilon$) $z=1/\tilde{\epsilon}T^{CG}-2\geq 2$ both for RSJ and TDGL and that the nonlinear IV exponent a is given by a=z+1 in the low-temperature phase. The results are discussed and compared with the results of other recent papers and the importance of the boundary conditions is emphasized.