https://doi.org/10.1140/epjp/s13360-026-07330-3
Regular Article
Geometric characterization of the phase transitions in a Blume-Capel model via the Ruppeiner metric
1
Institute of Science, Akdeniz University, 07058, Antalya, Turkey
2
Department of Physics, Akdeniz University, 07058, Antalya, Turkey
3
Department of Physics, Aydın Adnan Menderes University, 09010, Aydın, Turkey
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Received:
6
October
2025
Accepted:
14
January
2026
Published online:
12
February
2026
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 
. Notably, two half rings including the minima 
and maxima 
of R in the ferromagnetic phase are observed below the 
line. We also find that the separate 
and 
lines exist at higher temperatures within the paramagnetic phase. Under the effect of external magnetic field 
, these lines disappear and an additional curve appears just above the second-order phase transition line in the phase diagram.
© The Author(s) 2026
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