Equilibria when the temperature goes to zero

Abstract

We present methods to construct flows with varying sets of KMS infinity states on a given simple unital AF-algebra. It follows, for example, that for any pair D and E of non-empty compact metric spaces there is a flow on the CAR algebra whose set of KMS infinity states is homeomorphic to D while the set of KMS infinity states for the inverted flow is homeomorphic to E. Remarkably the flows that realize all such pairs D and E can be chosen to have isomorphic KMS bundles.

v3: Many minor corrections and other improvements. With a bit of luck the language has improved too. 37 pages. arXiv admin note: text overlap with arXiv:2204.01125