Generalized gauge actions on k-graph C^∗-algebras: KMS states and hausdorff structure

In this paper, we consider non-standard dynamics on the C^∗-algebra associated with a higher-rank graph Λ. These dynamics were first introduced by McNamara in his thesis, and arise from a functor y : Λ → R₊. We show that the KMS states associated with these dynamics are parametrized by the periodicity group of the higher-rank graph and a family of Borel probability measures on the infinite path space; an analogous parametrization was earlier obtained by Huef, Laca, Raeburn, and Sims in the case of the standard dynamics. The aforementioned Borel probability measures also arise as Hausdorff measures on the infinite path space of the higher-rank graph, and the associated Hausdorff dimension is intimately linked to the inverse temperatures at which KMS states exist. Our construction of the metrics underlying the Hausdorff structure uses the functors y, the stationary k-Bratteli diagram associated with Λ, and a new concept of exponentially self-similar weights on Bratteli diagrams.