The Phase Diagram of the Quantum Curie-Weiss Model

2008/04/10 by Lincoln Chayes, Nicholas Crawford, Dmitry Ioffe +1 · 1 citation
Mathematics · Physics and Astronomy · #Opinion Dynamics and Social Influence #Statistical Mechanics and Entropy #Theoretical and Computational Physics #math-ph #math.MP #math.PR #msc:82B10

paper · pdf · doi:10.1007/s10955-008-9608-x

20 pages/Removed Bracket from title

arxiv created 2008/04/10 · openalex publication_date 2008/08/28 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• On the critical behavior of the magnetization in high-dimensional Ising models
• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model

Cited by

• On quantum mean-field models and their quantum annealing