KMS states on the C*-algebras of finite graphs

TL;DR

This paper characterizes KMS states on the C*-algebras of finite graphs, providing explicit constructions for different temperature regimes and identifying unique states in strongly connected cases.

Contribution

It offers a direct, elementary method to construct all KMS states on Toeplitz-Cuntz-Krieger algebras of finite graphs, including the critical temperature case.

Findings

Explicit construction of KMS_{eta} states for eta > eta_c

Uniqueness of KMS_{eta_c} state for strongly connected graphs

KMS states factor through the graph C*-algebra at critical temperature

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 \beta_c, we give an explicit construction of all the KMS_{\beta} states. If the graph is strongly connected, then there is a unique KMS_{\beta_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.