Phase transition in the Connes-Marcolli GL2-system
  We develop a general framework for analyzing KMS-states on C*-algebras arising from actions of Hecke pairs. We then specialize to the system recently introduced by Connes and Marcolli and classify its KMS-states for inverse temperatures \beta\ne 0,1. In particular, we show that for each \beta\in(1,2] there exists a unique KMS_\beta-state. 
Marcelo Laca, Nadia Larsen, Sergey Neshveyev