Multicritical Points And Reentrant Phenomenon In The BEG Model

TL;DR

This paper investigates the phase transitions and reentrant phenomena in the Blume-Emery-Griffiths model using the cluster variation method, revealing different transition sequences depending on the quadrupole coupling sign.

Contribution

It introduces a detailed analysis of reentrant phenomena and phase diagrams in the BEG model using pair approximation, including equations for critical and tricritical lines.

Findings

Reentrant phenomena occur in two regions depending on the quadrupole coupling sign.

Different transition sequences are identified for positive and negative coupling.

Explicit equations for critical and tricritical lines are derived.

Abstract

The Blume - Emery - Griffiths model is investigated by use of the cluster variation method in the pair approximation. We determine the regions of the phase space where reentrant phenomenon takes place. Two regions are found, depending on the sign of the reduced quadrupole - quadrupole coupling strength $\xi$. For negative $\xi$ we find Para-Ferro-Para and Ferro-Para-Ferro-Para transition sequences; for positive $\xi$, a Para$_-$-Ferro-Para$_+$ sequence. Order parameters, correlation functions and specific heat are given in some typical cases. By-products of this work are the equations for the critical and tricritical lines.