Calculus of Variations and Geometric Measure Theory

A. Bach - M. Cicalese - L. Kreutz - G. Orlando

The antiferromagnetic XY model on the triangular lattice: topological singularities

created by orlando on 23 Nov 2020
modified by cicalese on 17 Sep 2023


Published Paper

Inserted: 23 nov 2020
Last Updated: 17 sep 2023

Journal: Indiana Univ. Mat. J.
Volume: 71
Pages: 2411–2475
Year: 2022

ArXiv: 2011.10445 PDF


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.