Reentrant Phase Transitions of the Blume-Emery-Griffiths Model for a Simple Cubic Lattice on the Cellular Automaton

TL;DR

This paper investigates reentrant phase transitions in the Blume-Emery-Griffiths model on a simple cubic lattice using an improved cellular automaton simulation, revealing complex phase behavior and comparing phase diagrams with other methods.

Contribution

It introduces an enhanced cellular automaton method to simulate the BEG model and explores reentrant phase transitions on a cubic lattice, providing new insights into phase diagrams.

Findings

Reentrant and double reentrant phase transitions identified.

Phase diagrams compared with other computational methods.

Simulation results show consistency with known phase behaviors.

Abstract

The spin-1 Ising (BEG) model with the nearest-neighbour bilinear and biquadratic interactions and single-ion anisotropy is simulated on a cellular automaton which improved from the Creutz cellular automaton(CCA) for a simple cubic lattice. The simulations have been made for several sets of parameters $K/J$ and $D/J$ in the $-3<D/J\leq 0$ and $-1\leq K/J\leq 0$ parameter regions. The re-entrant and double re-entrant phase transitions of the BEG model are determined from the temperature variations of the thermodynamic quantities ($M$, $Q$ and $\chi $). The phase diagrams characterizing phase transitions are compared with those obtained from other methods.