Thermodynamic versus statistical nonequivalence of ensembles for the mean-field Blume-Emery-Griffiths model

Abstract

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 characterization takes effect at the level of the microcanonical and canonical equilibrium distributions of states. For this reason it may be viewed as a statistical characterization of nonequivalent ensembles which extends and complements the common thermodynamic characterization of nonequivalent ensembles based on nonconcave anomalies of the microcanonical entropy. By computing numerically both the microcanonical and canonical sets of equilibrium distributions of states of the BEG model, we show that for values of the mean energy where the microcanonical entropy is nonconcave, the microcanonical distributions of states are nowhere realized in the canonical ensemble. Moreover, we show that for values of the mean energy where the microcanonical entropy is strictly concave, the equilibrium microcanonical distributions of states can be put in one-to-one correspondence with equivalent canonical equilibrium distributions of states. Our numerical computations illustrate general results relating thermodynamic and statistical equivalence and nonequivalence of ensembles proved by Ellis, Haven, and Turkington [J. Stat. Phys. 101, 999 (2000)].

arXiv comment13 pages, 4 figures, minor typos corrected and one reference added

References in corpus (5)

• Negative Specific Heat in Astronomy, Physics and Chemistry
• Inequivalence of ensembles in a system with long range interactions
• Violation of ensemble equivalence in the antiferromagnetic mean-field XY model
• First and second order clustering transitions for a system with infinite-range attractive interaction
• Nonequivalent ensembles and metastability

Cited by in corpus (50)

• The large deviation approach to statistical mechanics
• Statistical mechanics and dynamics of solvable models with long-range interactions
• An Introduction to the Thermodynamic and Macrostate Levels of Nonequivalent Ensembles
• Large deviation techniques applied to systems with long-range interactions
• Breaking of ensemble equivalence in networks
• Bose-Einstein condensation and gauge symmetry breaking
• Complete Analysis of Phase Transitions and Ensemble Equivalence for the Curie-Weiss-Potts Model
• Thermodynamic limits of dynamic cooling
• Fluctuations of composite observables and stability of statistical systems
• Partial equivalence of statistical ensembles and kinetic energy
• The generalized canonical ensemble and its universal equivalence with the microcanonical ensemble
• Generalized canonical ensembles and ensemble equivalence
• Dynamics and thermodynamics of rotators interacting with both long and short range couplings
• Negative magnetic susceptibility and nonequivalent ensembles for the mean-field ${\varphi }^4$ spin model
• Ensemble equivalence for general many-body systems
• Phase transitions in systems with non-additive long-range interactions
• Analysis of phase transitions in the mean-field Blume-Emery-Griffiths model
• Isotropic-Nematic Phase Transitions in Gravitational Systems
• Microcanonical solution of the mean-field ${\varphi }^4$ model: comparison with time averages at finite size
• Complete analysis of ensemble inequivalence in the Blume-Emery-Griffiths model
• Nonconcave entropies in multifractals and the thermodynamic formalism
• Ensemble nonequivalence in random graphs with modular structure
• Extended gaussian ensemble solution and tricritical points of a system with long-range interactions
• Algebraic Correlation Function and Anomalous Diffusion in the HMF model
• Multicanonical entropy like-solution of statistical temperature weighted histogram analysis method (ST-WHAM)
• Simple spin models with non-concave entropies
• Ensemble Inequivalence in the Ferromagnetic p-spin Model in Random Fields
• Generalized Gibbs ensembles for time dependent processes
• Phase diagram of the ABC model with nonconserving processes
• Non equivalence of dynamical ensembles and emergent non ergodicity
• Nonconcave entropies from generalized canonical ensembles
• Ensemble Inequivalence and the Spin-Glass Transition
• Methods for calculating nonconcave entropies
• Ensemble inequivalence : Landau theory and the ABC model
• Dynamical and statistical bimodality in nuclear fragmentation
• Shared information in classical mean-field models
• Metastability within the generalized canonical ensemble
• Rényi free energy and variational approximations to thermal states
• Comment on "First-order phase transitions: equivalence between bimodalities and the Yang-Lee theorem"
• Ensemble nonequivalence and Bose-Einstein condensation in weighted networks
• Ensemble Inequivalence in the Spherical Spin Glass Model with Nonlinear Interactions
• Many-body spin glasses in the microcanonical ensemble
• The extended gaussian ensemble and metastabilities in the Blume-Capel model
• Description length of canonical and microcanonical models
• A Simple Model for Long-Range Interacting Pendula
• Partial equivalence of statistical ensembles in a simple spin model with discontinuous phase transitions
• Ensemble Equivalence for Counterion Condensation on a Two Dimensional Charged Disc
• Fluids with power-law repulsion: Hyperuniformity and energy fluctuations
• Ensemble equivalence for mean field models and plurisubharmonicity
• Global optimization, the Gaussian ensemble, and universal ensemble equivalence