On Bost-Connes type systems for number fields

TL;DR

This paper provides a comprehensive analysis of phase transitions in Bost-Connes type systems for number fields, introduces K-lattices, and offers an interpretation in terms of 1-dimensional K-lattices, advancing understanding of these quantum statistical systems.

Contribution

It offers a complete description of phase transitions in Bost-Connes systems for number fields and introduces the concept of K-lattices with an interpretative framework.

Findings

Detailed phase transition characterization for Bost-Connes systems

Introduction of K-lattices concept

Interpretation of systems via 1-dimensional K-lattices

Abstract

We give a complete description of the phase transition of the Bost-Connes type systems for number fields recently introduced by Connes-Marcolli-Ramachandran and Ha-Paugam. We also introduce a notion of K-lattices and discuss an interpretation of these systems in terms of 1-dimensional K-lattices.