Ferromagnetism in the Blume-Emery-Griffiths model on finite-size Cayley tree

TL;DR

This paper investigates the ferromagnetic properties of the spin-1 BEG model on finite Cayley trees, revealing unique behaviors like anti-Curie temperature and providing insights into finite-size effects and thermodynamic limit convergence.

Contribution

The study applies exact recursion methods to analyze the finite-size Cayley tree, identifying novel magnetic behaviors and calculating critical temperatures for the BEG model.

Findings

Identification of anti-Curie temperature for D/J>2.0

Calculation of Curie temperature in finite systems

Finite-size results converge to thermodynamic limit

Abstract

The ferromagnetic properties of the spin-1 BEG model on finite-size Cayley tree are investigated using the exact recursion method. The spontaneous magnetization of the system is studied in detail for different values of the reduced crystal-field interaction D/J, and it is found that there is an unusual behavior (anti-Curie temperature) when D/J>2.0. We also obtain the Curie temperature of this finite-size system. When the system size is large enough, our results will fit well with that in the thermodynamic limit.