KMS states and branched points
Masaki Izumi, Tsuyoshi Kajiwara, Yasuo Watatani
Abstract
We completely classify the KMS states for the gauge action on a C*-algebra associated with a rational function R introduced in our previous work. The gauge action has a phase transition at β= °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*-algebras associated with some self-similar sets, including the full tent map and the Sierpinski gasket by a similar method.
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