KMS states on the C*-algebras of finite graphs
  We consider a finite directed graph E, and the gauge action on its Toeplitz-Cuntz-Krieger algebra, viewed as an action of R. For inverse temperatures larger than a critical value \beta_c, we give an explicit construction of all the KMS_{\beta} states. If the graph is strongly connected, then there is a unique KMS_{\beta_c} state, and this state factors through the quotient map onto the C*-algebra C*(E) of the graph. Our approach is direct and relatively elementary. 
Astrid an Huef, Marcelo Laca, Iain Raeburn, Aidan Sims
math.OA