2003/09/30 by Marek Biskup, L. Chayes, Lincoln Chayes +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Physics of Superconductivity and Magnetism #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP #math.PR
paper · pdf · doi:10.1007/s00220-004-1272-7
published as Commun. Math. Phys. 255 (2005), no. 2, 253-292 · 40 pages, 1 eps fig; a revised version correcting a bunch of small errors
arxiv created 2004/07/16 · openalex publication_date 2005/02/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the classical version of the 120-degree model. This is an attractive nearest-neighbor system in three dimensions with XY (rotor) spins and interaction such that only a particular projection of the spins gets coupled in each coordinate direction. Although the Hamiltonian has only discrete symmetries, it turns out that every constant field is a ground state. Employing a combination of spin-wave and contour arguments we establish the existence of long-range order at low temperatures. This suggests a mechanism for a type of ordering in certain models of transition-metal compounds where the very existence of long-range order has heretofore been a matter of some controversy.