2002/09/24 by J. -Ch. Anglès d'Auriac, J-Ch Angl s d Auriac, J-M Maillard +3
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Algorithm #Artificial intelligence #Computer science #Condensed matter physics #Enhanced Data Rates for GSM Evolution #Ising model #Physics #Potts model #Quantum many-body systems #Spin (aerodynamics) #State (computer science) #Statistical physics #Theoretical and Computational Physics #Thermodynamics #cond-mat.stat-mech #hep-th #nlin.SI
paper · pdf · doi:10.1088/0305-4470/35/44/301
5 figures
arxiv created 2002/09/24 · openalex publication_date 2002/10/21 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We classify four-state spin models with interactions along the edges according to their behaviour under a specific group of symmetry transformations. This analysis uses the measure of complexity of the action of the symmetries, in the spirit of the study of discrete dynamical systems on the space of parameters of the models, and aims at uncovering solvable ones. We find that the action of these symmetries has low complexity (polynomial growth, zero entropy). We obtain natural parametrizations of various models, among which an unexpected elliptic parametrization of the four-state chiral Potts model, which we use to localize possible integrability conditions associated with high genus curves.