2005/07/15 by Richard S. Ellis, Peter T. Otto, Hugo Touchette · 1 citation
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Statistical Mechanics and Entropy #Theoretical and Computational Physics #math.PR #msc:60F05 #msc:60F10 #msc:82B20
paper · pdf · doi:10.1214/105051605000000421
published as Annals of Applied Probability 2005, Vol. 15, No. 3, 2203-2254 · Published at http://dx.doi.org/10.1214/105051605000000421 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2005/07/15 · arxiv created 2005/08/25 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper we give a complete analysis of the phase transitions in the mean-field Blume–Emery–Griffiths lattice-spin model with respect to the canonical ensemble, showing both a second-order, continuous phase transition and a first-order, discontinuous phase transition for appropriate values of the thermodynamic parameters that define the model. These phase transitions are analyzed both in terms of the empirical measure and the spin per site by studying bifurcation phenomena of the corresponding sets of canonical equilibrium macrostates, which are defined via large deviation principles. Analogous phase transitions with respect to the microcanonical ensemble are also studied via a combination of rigorous analysis and numerical calculations. Finally, probabilistic limit theorems for appropriately scaled values of the total spin are proved with respect to the canonical ensemble. These limit theorems include both central-limit-type theorems, when the thermodynamic parameters are not equal to critical values, and noncentral-limit-type theorems, when these parameters equal critical values.