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 02 Apr 2021


Accepted Paper

Inserted: 23 nov 2020
Last Updated: 2 apr 2021

Journal: Indiana Univ. Mat. J.
Year: 2020

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.