Thermal phase transitions for Dicke-type models in the ultra-strong coupling limit

TL;DR

This paper investigates thermal phase transitions in Dicke-type models at finite particle numbers in the ultra-strong coupling limit, highlighting differences between bosonic and fermionic systems through explicit partition functions and free energy analysis.

Contribution

It provides explicit partition functions and Landau free energy expressions for Dicke models, revealing a crossover between fermionic and bosonic behaviors at finite particle numbers.

Findings

Identification of thermal phase transition signatures at finite N

Explicit derivation of partition functions with degeneracy factors

Observation of a crossover between fermionic and bosonic cases in specific heat

Abstract

We consider the Dicke model in the ultra-strong coupling limit to investigate thermal phase transitions and their precursors at finite particle numbers $N$ for bosonic and fermionic systems. We derive partition functions with degeneracy factors that account for the number of configurations and derive explicit expressions for the Landau free energy. This allows us to discuss the difference between the original Dicke (fermionic) and the bosonic case. We find a crossover between these two cases that shows up, e.g., in the specific heat.