Interaction of domain walls and vortices in the two-dimensional O(2) and O(3) principal chiral models

TL;DR

This study uses Monte Carlo simulations to explore how domain walls and vortices interact in two-dimensional O(2) and O(3) models, revealing non-universal vortex densities at the BKT transition and universal wall densities at the Ising transition.

Contribution

It provides new insights into defect interactions and their critical properties, especially under disorder conditions affecting both Ising and continuous symmetries.

Findings

Vortex density at BKT transition is non-universal.

Wall density at Ising transition remains universal.

Wall-vortex correlator tends to zero at the Ising point.

Abstract

Using extensive Monte Carlo simulations, we investigate the critical properties of domain walls, vortices and $\mathbb{Z}_2$ vortices in the Ising-$O(2)$ and Ising-$O(3)\otimes O(2)$ models. We have consider the nontrivial case when disorder in the Ising order parameter induces disorder in the continuous parameter. Such a situation arises when a domain wall becomes opaque for continuous parameter correlations. We find that in this case the vortex density at the BKT transition (or crossover) point turns out to be non-universal, while the wall density at the Ising transition remains universal, i.e. in agreement with the Ising model. An important part of this study is the numerical measurement of defect-defect correlators. We find that the wall-vortex correlator tends to zero in the thermodynamic limit at the Ising point, which explains the universality of the wall density. A possible multicritical behavior of the models is also discussed.