Eur. Phys. J. B 75, 311-318 (2010)
https://doi.org/10.1140/epjb/e2010-00161-y

Extended gaussian ensemble solution and tricritical points of a system with long-range interactions

¹ Departamento de Física e Matemática, FFCLRP, Universidade de São Paulo, Avenida Bandeirantes 3900, CEP 14040-901 Ribeirão Preto, SP, Brazil
² Universidade Tecnológica Federal do Paraná, Rua XV de Novembro 2191, CEP 85902-040, Toledo, PR, Brazil

Corresponding author: ^a alves@ffclrp.usp.br

Received: 23 December 2009
Revised: 17 March 2010
Published online: 26 May 2010

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.