%0 Journal Article
%T Phase transitions on the Toeplitz algebras of Baumslag-Solitar semigroups
%A Lisa Orloff Clark
%A Astrid an Huef
%A Iain Raeburn
%J Mathematics
%D 2015
%I arXiv
%X Spielberg has recently shown that Baumslag-Solitar groups associated to pairs of positive integers are quasi-lattice ordered in the sense of Nica. Thus they have tractable Toeplitz algebras. Each of these algebras carries a natural dynamics. Here we construct the equilibrium states (the KMS states) for these dynamics. For inverse temperatures larger than a critical value, there is a large simplex of KMS states parametrised by probability measures on the unit circle. At the critical value, and under a mild hypothesis, there is a phase transition in which this simplex collapses to a singleton. There is a further phase transition at infinity, in the sense that there are many ground states which cannot be realised as limits of KMS states with finite inverse temperatures.
%U http://arxiv.org/abs/1503.04873v1