Abstract The thermodynamic geometry based on the Ruppeiner formalism is utilized to investigate the spin-1 Blume-Capel model in the absence and presence of the external magnetic field (h). An explicit expression for the thermodynamic curvature or Ricci scalar (R) is derived. Its behaviour near the critical and tricritical points and a geometric phase diagram highlighting the characteristics of R are presented when h=0 h = 0. Notably, two half rings including the minima (RM) (R M) and maxima (RP) (R P) of R in the ferromagnetic phase are observed below the R=0 R = 0 line. We also find that the separate RM R M and RP R P lines exist at higher temperatures within the paramagnetic phase. Under the effect of external magnetic field (h 0) (h ≠ 0), these lines disappear and an additional RP R P curve appears just above the second-order phase transition line in the phase diagram.
Akkurt et al. (Thu,) studied this question.