2011/06/15 by Artur O. Lopes, Lopes, Artur O., Jairo K. Mengue +2
Mathematics · Physics and Astronomy · #37A05 #37A50 #37A60 #82B05 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.DS #math.MP #math.PR #msc:37A05 #msc:37A50 #msc:37A60 #msc:82B05
paper · pdf · doi:10.48550/arxiv.1106.3118
openalex publication_date 2011/06/15 · arxiv created 2013/08/12 · arxiv updated 2013/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider (M,d) a connected and compact manifold and we denote by X the Bernoulli space Mℕ. The shift acting on X is denoted by σ. We analyze the general XY model, as presented in a recent paper by A. T. Baraviera, L. M. Cioletti, A. O. Lopes, J. Mohr and R. R. Souza. Denote the Gibbs measure by μc:=hcνc, where hc is the eigenfunction, and, νc is the eigenmeasure of the Ruelle operator associated to cf. We are going to prove that any measure selected by μc, as c→ +∞, is a maximizing measure for f. We also show, when the maximizing probability measure is unique, that it is true a Large Deviation Principle, with the deviation function R+∞=∑j=0^∞ R+ (σf), where R+:= β(f) + V∘σ- V - f, and, V is any calibrated subaction.