Geometrical aspects of the multicritical phase diagrams for the Blume-Emery-Griffiths model

As a continuation of our preceding work (Erdem and Alata in Eur Phys J Plus 135:911, 2020, https://doi.org/10.1140/epjp/ s13360-020-00934-3), we used the thermodynamic geometry in the Ruppeiner formalism to study the geometrical aspects of the multicritical phase diagrams for the spin-1 Blume-Emery-Griffiths model in the presence of crystal field. We derived an expression for the thermodynamic curvature or Ricci scalar (R) and analyzed its temperature and crystal field behaviours near interesting critical and multicritical points. Our findings are presented as geometrical phase diagrams including critical and multicritical topology. From these diagrams, new vanishing curvature lines (R = 0) extending into the ferromagnetic or paramagnetic phases beyond the critical points and zero point temperature are observed.