Thermodynamic geometry of Ising ferromagnet in an external magnetic field: A self-consistent field theory calculation
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, vol.526, 2019 (SCI-Expanded)
- Publication Type: Article / Article
- Volume: 526
- Publication Date: 2019
- Doi Number: 10.1016/j.physa.2019.121173
- Journal Name: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Keywords: Thermodynamic curvature, Ferromagnetic Ising model, Pair approximation, Self-consistent field theory, INFORMATION GEOMETRY, RIEMANNIAN GEOMETRY, PHASE-DIAGRAMS, MODEL, RELAXATION, FRAMEWORK
- Akdeniz University Affiliated: Yes
Abstract
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.