Vortex annihilation in the ordering kinetics of the O(2) model

TL;DR

This paper investigates vortex interactions during phase ordering in the 2D O(2) model, comparing theoretical correlation functions with simulations, revealing both agreements and discrepancies at different scales.

Contribution

It provides analytical vortex correlation functions and compares them with simulations, highlighting the behavior of vortex annihilation and interactions in the model.

Findings

Good agreement for vortex-vortex correlation at intermediate distances

Vortex-antivortex correlation matches simulations at large scales

Discrepancy at short distances with a depletion zone not captured by theory

Abstract

The vortex-vortex and vortex-antivortex correlation functions are determined for the two-dimensional O(2) model undergoing phase ordering. We find reasonably good agreement with simulation results for the vortex-vortex correlation function where there is a short-scaled distance depletion zone due to the repulsion of like-signed vortices. The vortex-antivortex correlation function agrees well with simulation results for intermediate and long-scaled distances. At short-scaled distances the simulations show a depletion zone not seen in the theory.