The Phase Diagram of the Quantum Curie-Weiss Model

TL;DR

This paper explores the phase diagram of a quantum version of the Curie-Weiss model, revealing how quantum effects influence phase transitions and critical behavior in a mean-field setting.

Contribution

It provides a complete characterization of the phase diagram for the quantum Curie-Weiss model using probabilistic methods, including critical exponents and stability analysis.

Findings

Identified the phase boundaries in the quantum model.

Calculated the critical exponent for order parameter decay.

Established stability properties of the associated variational problem.

Abstract

This paper studies a generalization of the Curie-Weiss model (the Ising model on a complete graph) to quantum mechanics. Using a natural probabilistic representation of this model, we give a complete picture of the phase diagram of the model in the parameters of inverse temperature and transverse field strength. Further analysis computes the critical exponent for the decay of the order parameter in the approach to the critical curve and gives useful stability properties of a variational problem associated with the representation.