Finite-Size Scaling and Power Law Relations for Dipol-Quadrupol Interaction on Blume-Emery-Griffiths Model

TL;DR

This paper investigates the finite-size scaling and power law relations of the dipol-quadrupol interaction in the Blume-Emery-Griffiths model using cellular automaton simulations on an fcc lattice, revealing that the interaction acts like an external magnetic field.

Contribution

It introduces finite-size scaling relations and estimates the critical exponent for the dipol-quadrupol interaction in the BEG model, showing its similarity to an external magnetic field.

Findings

The dipol-quadrupol interaction behaves like an external magnetic field.

Critical exponent elta_{\u00b5} matches the universal value of 5.

Finite-size scaling relations are established for the model.

Abstract

The Blume-Emery-Griffiths model with the dipol-quadrupol interaction (\ell) has been simulated using a cellular automaton algorithm improved from the Creutz cellular automaton (CCA) on the face centered cubic (fcc) lattice. The finite-size scaling relations and the power laws of the order parameter (M) and the susceptibility (\chi) are proposed for the dipol-quadrupol interaction (\ell). The dipol-quadrupol critical exponent \delta_{\ell} has been estimated from the data of the order parameter (M) and the susceptibility (\chi). The simulations have been done in the interval 0\leq \ell =L/J\leq 0.01 for d=D/J=0, k=K/J=0 and h=H/J=0 parameter values on a face centered cubic (fcc) lattice with periodic boundary conditions. The results indicates that the effect of the \ell parameter is similar to the external magnetic field (h). The critical exponent \delta_{\ell}$ are in good agreement with the universal value (\delta_{h}=5) of the external magnetic field.