The antiferromagnetic XY model on the triangular lattice: topological singularities

TL;DR

This paper analyzes the antiferromagnetic XY model on a triangular lattice, deriving a continuum limit that captures vortex singularities and the dominance of a single chirality phase in the vortex regime.

Contribution

It provides an explicit computation of the Gamma-limit of the scaled energy, revealing vortex-like singularities and the behavior of the order parameter in the majority chirality phase.

Findings

Gamma-limit concentrates on vortex singularities

Order parameter describes vortex structure in the dominant chirality phase

Explicit characterization of the vortex regime in the antiferromagnetic XY model

Abstract

We study the discrete-to-continuum variational limit of the antiferromagnetic XY model on the two-dimensional triangular lattice in the vortex regime. Within this regime, the spin system cannot overcome the energetic barrier of chirality transitions, hence one of the two chirality phases is prevalent. We find the order parameter that describes the vortex structure of the spin field in the majority chirality phase and we compute explicitly the $\Gamma$-limit of the scaled energy, showing that it concentrates on finitely many vortex-like singularities of the spin field.