KMS states and branched points

Details KMS states and branched points KMS states and branched points

2006-03-25

arxiv.org/abs/math/0603592v1

Mathematics

Operator Algebras

32 pages, LaTeX2e formated

Scientific paper

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 $\beta = \log \deg R$. 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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