Ruppeiner geometry of isotropic Blume-Emery-Griffiths model

TL;DR

This paper uses Ruppeiner thermodynamic geometry to analyze phase transitions in the isotropic Blume-Emery-Griffiths model, revealing divergence, jumps, and extrema in the Ricci scalar near critical points.

Contribution

It derives an explicit Ricci scalar expression for the model and studies its temperature behavior across different phase transition regimes.

Findings

Ricci scalar diverges at continuous phase transitions.

Finite jumps in Ricci scalar occur at discontinuous transitions.

Broad extrema in Ricci scalar are field-dependent near critical points.

Abstract

With the aid of Ruppeiner thermodynamic metric defined on a two-dimensional phase space of dipolar ($m$) and quadrupolar ($q$) order parameters, we derive an expression for the Ricci scalar ($R$) in the isotropic Blume-Emery-Griffiths model. Temperature dependence of $R$ is investigated for various values of bilinear to biquadratic ratio ($r$). Its behavior near the continuous/discontinuous phase transition temperatures and a tricritical point is presented. It is found that in addition to the divergence singularity and finite jumps connected with the phase transitions there are field-dependent broad extrema in the Ricci scalar.