The extended gaussian ensemble and metastabilities in the Blume-Capel model
arXiv:1006.0708 · doi:10.1088/1742-6596/246/1/012018
Abstract
The Blume-Capel model with infinite-range interactions presents analytical solutions in both canonical and microcanonical ensembles and therefore, its phase diagram is known in both ensembles. This model exhibits nonequivalent solutions and the microcanonical thermodynamical features present peculiar behaviors like nonconcave entropy, negative specific heat, and a jump in the thermodynamical temperature. Examples of nonequivalent ensembles are in general related to systems with long-range interactions that undergo canonical first-order phase transitions. Recently, the extended gaussian ensemble (EGE) solution was obtained for this model. The gaussian ensemble and its extended version can be considered as a regularization of the microcanonical ensemble. They are known to play the role of an interpolating ensemble between the microcanonical and the canonical ones. Here, we explicitly show how the microcanonical energy equilibrium states related to the metastable and unstable canonical solutions for the Blume-Capel model are recovered from EGE, which presents a concave "extended" entropy as a function of energy.
6 pages, 5 eps figures. Presented at the XI Latin American Workshop on Nonlinear Phenomena, October 05-09 (2009), Búzios (RJ), Brazil. To appear in JPCS
References in corpus (14)
- Breaking of ergodicity and long relaxation times in systems with long-range interactions
- Classification of phase transitions and ensemble inequivalence, in systems with long range interactions
- Large deviation techniques applied to systems with long-range interactions
- Thermodynamic versus statistical nonequivalence of ensembles for the mean-field Blume-Emery-Griffiths model
- When is a quantity additive, and when is it extensive?
- 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
- Negative magnetic susceptibility and nonequivalent ensembles for the mean-field spin model
- Statistical Mechanics in the Extended Gaussian Ensemble
- Extended gaussian ensemble solution and tricritical points of a system with long-range interactions
- Nonconcave entropies from generalized canonical ensembles
- Metastability within the generalized canonical ensemble
- Equilibrium and nonequilibrium properties of systems with long-range interactions