Mean and Gaussian curvatures of equilibrium states for a spin-1 Ising system: existence of minimal surface in the paramagnetic solutions

ERDEM R.

European Physical Journal Plus, cilt.138, sa.4, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 138 Sayı: 4
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1140/epjp/s13360-023-03925-2
  • Dergi Adı: European Physical Journal Plus
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC
  • Akdeniz Üniversitesi Adresli: Evet

Özet

We present an approach to analyze the equilibrium states in a spin-1 Ising model with bilinear and biquadratic interactions using mean (H) and Gaussian (K) curvatures of the mean-field free energy surface. From the temperature variation of H and K, we have reported the local shapes of equilibrium free energies for the paramagnetic, ferromagnetic and quadrupolar solutions. It is important to mention that a minimal surface for the paramagnetic case with H= 0 , K< 0 is explicitly observed. For the ferromagnetic case, it is found that the curvature H displays a cusp singularity at the criticality with the exponent values of (λH,λH′)=(0,1) and a convergence of K is observed with λK= 1.0.