Thermodynamic geometry of Ising ferromagnet in an external magnetic field: A self-consistent field theory calculation

ERDEM R.

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, cilt.526, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 526
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1016/j.physa.2019.121173
  • Dergi Adı: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Thermodynamic curvature, Ferromagnetic Ising model, Pair approximation, Self-consistent field theory, INFORMATION GEOMETRY, RIEMANNIAN GEOMETRY, PHASE-DIAGRAMS, MODEL, RELAXATION, FRAMEWORK
  • Akdeniz Üniversitesi Adresli: Evet

Özet

We present a complete geometrical description for the ferromagnetic Ising model in the pair approximation as introduced by Balcerzak (2003) using self-consistent field theory. A metric is defined in a two-dimensional phase space of magnetization (M) and nearest neighbour correlation function (C). Based on the metric elements an expression for the thermodynamic Ricci scalar (R) is derived in terms of the lattice coordination number q. We study R as the temperature (T), magnetic field (h) and exchange energy coupling (J) are varied and show that there are T and h dependent critical properties for q = 6. By direct comparison, we demonstrate that the special case q = 2 provides a consistent behaviour with the already known exact formula in Janyszek and Mrugala work (1989) for the one-dimensional Ising model. (C) 2019 Elsevier B.V. All rights reserved.