The Antiferromagnetic XY Model on the Triangular Lattice: Topological Singularities

Annika Bach, Marco Cicalese, Leonard Kreutz, Gianluca Orlando

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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, and 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 Γ-limit of the scaled energy, showing that it concentrates on finitely many vortex-like singularities of the spin field.

Original languageEnglish
Pages (from-to)2411-2475
Number of pages65
JournalIndiana University Mathematics Journal
Issue number6
StatePublished - 2022


  • Gamma-convergence
  • frustrated lattice systems
  • topological singularities


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