Abstract
We present methods to construct flows with varying set of KMS∞ states on a given simple unital AF-algebra. It follows, for example, that for any pair D+ and D− of non-empty compact metric spaces there is a flow σ=(σt)t∈R on the CAR algebra whose set of KMS∞ states is homeomorphic to D+ while the set of KMS∞ states for the inverted flow (σ−t)t∈R is homeomorphic to D−. Remarkably the flows that realize all such pairs D± can be chosen to have isomorphic KMS bundles.
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