Blume-Emery-Griffiths Model in a Random Crystal Field

TL;DR

This paper investigates how disorder affects phase transitions in the Blume-Emery-Griffiths model using renormalization-group and mean-field methods, revealing that disorder can change the nature of phase transitions.

Contribution

It compares the effects of disorder on phase transitions in the model using two different theoretical approaches, highlighting their differing predictions.

Findings

Disorder eliminates non-symmetry-breaking first-order transitions in 2D renormalization-group analysis.

Mean-field results show first-order transitions persist despite disorder.

Discussions include implications for martensitic transitions related to degeneracy parameters.

Abstract

We study the Blume-Emery-Griffiths model in a random crystal field in two and three dimensions, through a real-space renormalization-group approach and a mean-field approximation, respectively. According to the two-dimensional renormalization-group calculation, non-symmetry-breaking first-order phase transitions are eliminated and symmetry-breaking discontinuous transitions are replaced by continuous ones, when disorder is introduced. On the other hand, the mean-field calculation predicts that first-order transitions are not eliminated by disorder, although some changes are introduced in the phase diagrams. We make some comments on the consequences of a degeneracy parameter, which may be relevant in martensitic transitions.