2000/12/31 by Jürg Fröhlich, J. Froehlich, Luc Rey-Bellet +3 · 14 citations
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Continuous symmetry #Diagonal #Discrete symmetry #Explicit symmetry breaking #Geometry #Homogeneous space #Lattice (music) #Mathematics #Physics #Quantum #Quantum many-body systems #Quantum mechanics #Spontaneous symmetry breaking #Symmetry (geometry) #Symmetry breaking #Theoretical and Computational Physics #math-ph #math.MP #msc:82B10
paper · pdf · doi:10.1007/s002200100530
published in Communications in Mathematical Physics 224(1), 33-63 (Springer Science+Business Media) · 25 pages, 6 figures
arxiv created 2001/07/14 · openalex publication_date 2001/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We analyze the free energy and construct the Gibbs-KMS states for a class of quantum lattice systems, at low temperatures and when the interactions are almost diagonal in a suitable basis. We study systems with continuous symmetry, but our results are valid for discrete symmetry breaking only. Such phase transitions occur at intermediate temperatures where the continuous symmetry is not broken, while at very low temperature continuous symmetry breaking may occur.