A complete characterization is given of the collection of KMS state spaces for a flow on the Jiang-Su C*-algebra in the case that the set of inverse temperatures is bounded. Namely, it is an arbitrary compact simplex bundle over the (compact) set of inverse temperatures with fibre at zero a single point. (Hence this holds for the tensor product of this C*-algebra with any unital C*-algebra with unique trace state.) An analogous characterization is given for arbitrary flows on a (Kirchberg–Phillips) classifiable infinite unital simple C*-algebra: for each such algebra the KMS states form an arbitrary proper simplex bundle (the inverse image of a compact set of inverse temperatures is compact) such that the fibre at zero is empty.
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