KMS states and branched points

Abstract

We completely classify the KMS states for the gauge action on a $C^{\ast }$-algebra associated with a rational function $R$ introduced in our previous work. The gauge action has a phase transition at $\beta =\log °R$. We can recover the degree of $R$, the number of branched points, the number of exceptional points and the orbits of exceptional points from the structure of the KMS states. We also classify the KMS states for $C^{\ast }$-algebras associated with some self-similar sets, including the full tent map and the Sierpinski gasket by a similar method.

32 pages, LaTeX2e formated

References in corpus (2)

• KMS states of quasi-free dynamics on Pimsner algebras
• C*-algebras associated with branched coverings