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Nonconcave entropies from generalized canonical ensembles
Marius Costeniuc, Richard S. Ellis, Hugo Touchette
It is well-known that the entropy of the microcanonical ensemble cannot be calculated as the Legendre transform of the canonical free energy when the entropy is nonconcave. To circ…
Generalized canonical ensembles and ensemble equivalence
M. Costeniuc, R. S. Ellis, H. Touchette +1
This paper is a companion article to our previous paper (J. Stat. Phys. 119, 1283 (2005), cond-mat/0408681), which introduced a generalized canonical ensemble obtained by multiplyi…
Complete Analysis of Phase Transitions and Ensemble Equivalence for the Curie-Weiss-Potts Model
Marius Costeniuc, Richard S. Ellis, Hugo Touchette
Using the theory of large deviations, we analyze the phase transition structure of the Curie-Weiss-Potts spin model, which is a mean-field approximation to the Potts model. This an…
Analysis of phase transitions in the mean-field Blume-Emery-Griffiths model
R. S. Ellis, P. Otto, H. Touchette
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…
The generalized canonical ensemble and its universal equivalence with the microcanonical ensemble
M. Costeniuc, R. S. Ellis, H. Touchette +1
Shortened abstract: Microcanonical equilibrium macrostates are characterized as the solutions of a constrained minimization problem, while canonical equilibrium macrostates are cha…
Thermodynamic versus statistical nonequivalence of ensembles for the mean-field Blume-Emery-Griffiths model
Richard S. Ellis, Hugo Touchette, Bruce Turkington
We illustrate a novel characterization of nonequivalent statistical mechanical ensembles using the mean-field Blume-Emery-Griffiths (BEG) model as a test model. The novel character…