KMS states on the C∗-algebras of finite graphs

By Astrid an Huef, Marcelo Laca, Iain Raeburn, Aidan Sims. 2012

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Abstract We consider a finite directed graph E , and the gauge action on its Toeplitz–Cuntz–Krieger algebra, viewed as an action of R . For inverse temperatures larger than a critical value β c , we give an explicit construction of all the KMS β states. If the graph is strongly connected, then there is a unique KMS β c state, and this state factors through the quotient map onto C ∗ ( E ) . Our approach is direct and relatively elementary.

Subfields: Algebra and Number Theory, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/37306babf2c31a46a9f3e16e30a365b833908b01