The extended gaussian ensemble and metastabilities in the Blume-Capel model

TL;DR

This paper explores how the extended gaussian ensemble (EGE) can recover microcanonical metastable and unstable states in the Blume-Capel model, highlighting its role as an interpolating ensemble between microcanonical and canonical descriptions.

Contribution

It demonstrates explicitly how the EGE regularizes the microcanonical ensemble and recovers metastable and unstable states in the Blume-Capel model with long-range interactions.

Findings

EGE recovers microcanonical metastable states

EGE provides a concave extended entropy function

EGE acts as an interpolating ensemble

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.