2006/03/27 by W D Heiss, WD Heiss
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Hamiltonian (control theory) #Hermitian matrix #Limit (mathematics) #Phase transition #Spectral Theory in Mathematical Physics #Theoretical and Computational Physics #Thermodynamic beta #Thermodynamic limit #Thermodynamic potential #Thermodynamic process #quant-ph
paper · pdf · doi:10.1088/0305-4470/39/32/s10
9 pages, 3 figures to appear in JPhysA
arxiv created 2006/03/27 · openalex publication_date 2006/07/26 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The thermodynamic limit of the Lipkin model is investigated. While the limit turns out to be rather elusive, the analysis gives strong indications that the limit yields two analytically dissociated operators, one for the normal and one for the deformed phase. While the Lipkin Hamiltonian is Hermitian and has a second-order phase transition in finite dimensions (finite particle number), both properties seem to be destroyed in the thermodynamic limit.