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- Title
Extended gaussian ensemble solution and tricritical points of a system with long-range interactions.
- Authors
Frigori, R. B.; Rizzi, L. G.; Alves, N. A.
- Abstract
The gaussian ensemble and its extended version theoretically play the important role of interpolating ensembles between the microcanonical and the canonical ensembles. Here, the thermodynamic properties yielded by the extended gaussian ensemble (EGE) for the Blume-Capel (BC) model with infinite-range interactions are analyzed. This model presents different predictions for the first-order phase transition line according to the microcanonical and canonical ensembles. From the EGE approach, we explicitly work out the analytical microcanonical solution. Moreover, the general EGE solution allows one to illustrate in details how the stable microcanonical states are continuously recovered as the gaussian parameter γ is increased. We found out that it is not necessary to take the theoretically expected limit γ → ∞ to recover the microcanonical states in the region between the canonical and microcanonical tricritical points of the phase diagram. By analyzing the entropy as a function of the magnetization we realize the existence of unaccessible magnetic states as the energy is lowered, leading to a breaking of ergodicity.
- Subjects
GAUSSIAN processes; MATHEMATICAL models; CANONICAL correlation (Statistics); THERMODYNAMICS; STOCHASTIC processes
- Publication
European Physical Journal B: Condensed Matter, 2010, Vol 75, Issue 3, p311
- ISSN
1434-6028
- Publication type
Article
- DOI
10.1140/epjb/e2010-00161-y