KMS states on the C*-algebras of finite graphs

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 the C*-algebra C*(E) of the graph. Our approach is direct and relatively elementary.

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