2014/02/03 by Astrid an Huef, Huef, Astrid an, Marcelo Laca +5
Mathematics · Physics and Astronomy · #46L30 #Advanced Operator Algebra Research #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #Quantum many-body systems
paper · pdf · doi:10.48550/arxiv.1402.0276
openalex publication_date 2014/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the dynamics on the C*-algebras of finite graphs obtained by lifting the gauge action to an action of the real line. Enomoto, Fujii and Watatani proved that if the vertex matrix of the graph is irreducible, then the dynamics on the graph algebra admits a single KMS state. We have previously studied the dynamics on the Toeplitz algebra, and explicitly described a finite-dimensional simplex of KMS states for inverse temperatures above a critical value. Here we study the KMS states for graphs with reducible vertex matrix, and for inverse temperatures at and below the critical value. We prove a general result which describes all the KMS states at a fixed inverse temperature, and then apply this theorem to a variety of examples. We find that there can be many patterns of phase transition, depending on the behaviour of paths in the underlying graph.