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Full-Text Articles in Physical Sciences and Mathematics
Analysis Of Phase Transitions In The Mean-Field Blume-Emery-Griffiths Model, Rs Ellis, Pt Otto, H Touchette
Analysis Of Phase Transitions In The Mean-Field Blume-Emery-Griffiths Model, Rs Ellis, Pt Otto, H Touchette
Mathematics and Statistics Department Faculty Publication Series
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 …
Large Deviation Principles And Complete Equivalence And Nonequivalence Results For Pure And Mixed Ensembles, Rs Ellis, K Haven, B Turkington
Large Deviation Principles And Complete Equivalence And Nonequivalence Results For Pure And Mixed Ensembles, Rs Ellis, K Haven, B Turkington
Mathematics and Statistics Department Faculty Publication Series
We consider a general class of statistical mechanical models of coherent structures in turbulence, which includes models of two-dimensional fluid motion, quasi-geostrophic flows, and dispersive waves. First, large deviation principles are proved for the canonical ensemble and the microcanonical ensemble. For each ensemble the set of equilibrium macrostates is defined as the set on which the corresponding rate function attains its minimum of 0. We then present complete equivalence and nonequivalence results at the level of equilibrium macrostates for the two ensembles. Microcanonical equilibrium macrostates are characterized as the solutions of a certain constrained minimization problem, while canonical equilibrium macrostates …