The Ising Model on the Bethe Lattice with Two Atoms Per Site
SPIN, vol.14, no.04, 2024 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 14 Issue: 04
- Publication Date: 2024
- Doi Number: 10.1142/s2010324724500140
- Journal Name: SPIN
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Keywords: Molecule, spin, Ising model, Bethe lattice, recursion relations, phase diagram
- Erciyes University Affiliated: Yes
Abstract
The molecular approach of a spin model is constructed on the Bethe lattice (BL), and then it is examined in terms of exact recursion relations. Rather than assuming that each BL site is inhabited by a single spin, each site is occupied by two spin-1/2 atoms A and B, forming a molecule. Each molecule is considered to contain two spin-1/2 atoms, as well as q=3,4, or 6 nearest-neighbor molecules. In addition to the internal interactions between the atoms of each molecule, the molecules interact via their atoms in terms of bilinear interaction parameters J. Atoms of a molecule interact with JAiBi, while the molecules interact via their atoms in terms of JAiBi+1=JBiAi+1 and JAiAi+1=JBiBi+1. After obtaining the magnetizations of each atom in the central molecule of the BL, the average magnetization of the molecule is determined. It is found that the model presents first-and second-order and random phase transitions. The model also displays tricritical, bicritical and end points, in addition to reentrant behavior for appropriate J values.