In order to realize all possible KMS-bundles on the Jiang–Su algebra, we introduce a class of C^* -algebras which we call rationally approximately finite-dimensional (RAF). Using these, we show that for a given proper simplex bundle (S, ) with a singleton ^-1 (\0\) and a unital separable monotracial C^* -algebra A absorbing the Jiang–Su algebra tensorially (for instance, the irrational rotation algebra), there exists a flow on A whose KMS-bundle is isomorphic to (S, ).
Elliott et al. (Fri,) studied this question.