The possible temperatures for flows on a simple AF algebra

TL;DR

This paper demonstrates that for any infinite dimensional simple unital AF algebra and any closed lower bounded set of real numbers containing zero, there exists a flow on the algebra with that set as the possible inverse temperatures.

Contribution

It constructs flows on AF algebras with prescribed sets of inverse temperatures, expanding understanding of thermodynamic properties in operator algebras.

Findings

Existence of flows with arbitrary prescribed inverse temperature sets.

Construction applicable to any infinite dimensional simple unital AF algebra.

Sets of inverse temperatures can be any closed lower bounded set containing zero.

Abstract

It is shown that for any infinite dimensional simple unital AF algebra A and any closed lower bounded set K of real numbers containing zero there is a flow on A for which the set of possible inverse temperatures is K.