Dynamic critical behaviors of three-dimensional XY models related to superconductors/superfluids

TL;DR

This paper investigates the dynamic critical exponent z in three-dimensional XY models with different dynamics and boundary conditions, providing insights relevant to superconductors and superfluids.

Contribution

It presents numerical estimates of the dynamic critical exponent z for various dynamics and boundary conditions in 3D XY models, connecting results to superfluid and superconductor physics.

Findings

z ≈ 2 for relaxational dynamics with PBC

z ≈ 1.5 for relaxational dynamics with FTBC

z ≈ 1.5 for RSJ dynamics in both boundary conditions

Abstract

The dynamic critical exponent z is determined from numerical simulations for the three-dimensional XY model subject to two types of dynamics, i.e. relaxational dynamics and resistively shunted junction (RSJ) dynamics, as well as for two different treatments of the boundary, i.e., periodic boundary condition (PBC) and fluctuating twist boundary condition (FTBC). In case of relaxational dynamics, finite size scaling at the critical temperature gives $z\approx 2$ for PBC and 1.5 for FTBC, while for RSJ dynamics $z\approx 1.5$ is obtained in both cases. The results are discussed in the context of superfluid/superconductors and vortex dynamics, and are compared with what have been found for other related models.