Equilibria when the temperature goes to zero

TL;DR

This paper develops methods to construct flows on AF-algebras with prescribed sets of KMS infinity states, demonstrating the flexibility of KMS state structures and their invariance under flow inversion.

Contribution

It introduces a novel approach to realize any pair of compact metric spaces as KMS infinity state sets on AF-algebras, with flows having isomorphic KMS bundles.

Findings

Constructed flows with prescribed KMS infinity states.

Showed the existence of flows with homeomorphic KMS state sets to any given pair of compact metric spaces.

Established that such flows can have isomorphic KMS bundles.

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.