2009/09/30 by Michael Kästner, Michael Kastner
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Antiferromagnetism #Canonical ensemble #Condensed matter physics #Configuration entropy #Entropy (arrow of time) #Ferromagnetism #Ising model #Mathematics #Microcanonical ensemble #Phase (matter) #Phase diagram #Physics #Quantum mechanics #Residual entropy #Spherical model #Spins #Statistical Mechanics and Entropy #Statistical physics #Theoretical and Computational Physics #Thermodynamic limit #cond-mat.stat-mech #k-nearest neighbors algorithm
paper · pdf · doi:10.1088/1742-5468/2009/12/p12007
published as Journal of Statistical Mechanics: Theory and Experiment (2009) P12007 · 14 pages, 6 figures
openalex publication_date 2009/12/10 · arxiv created 2009/12/11 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
For the spherical model with nearest-neighbour interactions, the microcanonical entropy s (ε, m ) is computed analytically in the thermodynamic limit for all accessible values of the energy ε and the magnetization m per spin. The entropy function is found to be concave (albeit not strictly concave), implying that the microcanonical and the canonical ensembles are equivalent, despite the long-range nature of the spherical constraint that the spins have to obey. Two transition lines are identified in the (ε, m )-plane, separating a paramagnetic phase from a ferromagnetic and an antiferromagnetic one. The resulting microcanonical phase diagram is compared to the more familiar canonical one.