On the possible temperatures for flows on an AF algebra

TL;DR

This paper constructs a specific AF algebra with a family of flows whose inverse temperatures cover any chosen compact set containing zero, with unique equilibrium states at each temperature.

Contribution

It introduces a unital simple mono-tracial AF algebra capable of supporting flows with prescribed inverse temperature sets, a novel construction in operator algebras.

Findings

Existence of flows with prescribed inverse temperature sets

Unique equilibrium states at each temperature

Construction of a specialized AF algebra

Abstract

We exhibit a unital simple mono-tracial AF algebra A with the property that for any compact set K of real numbers containing 0 there is a periodic flow on A such the set of possible inverse temperatures for that flow is K, and for each number in K the corresponding equilibrium state is unique.