Analysis of phase transitions in the mean-field Blume-Emery-Griffiths model

• 成果类型: Article
• 署名作者: Ellis, RS; Otto, PT; Touchette, H
• 署名单位: University of Massachusetts System; University of Massachusetts Amherst; Union College; University of London; Queen Mary University London
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051605000000421
• 发表日期: 2005
• 页码: 2203-2254
• 关键词: lattice-gas model; statistical-mechanics; LIMIT-THEOREMS; ising systems; triplet ions; nonequivalence; condensation; SEPARATION; ensembles; binary

摘要

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.