Mean and Gaussian curvatures of equilibrium states for a spin-1 Ising system: existence of minimal surface in the paramagnetic solutions
European Physical Journal Plus, vol.138, no.4, 2023 (SCI-Expanded)
- Publication Type: Article / Article
- Volume: 138 Issue: 4
- Publication Date: 2023
- Doi Number: 10.1140/epjp/s13360-023-03925-2
- Journal Name: European Physical Journal Plus
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC
- Akdeniz University Affiliated: Yes
Abstract
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.