Critical behavior and phase diagrams of a spin-1 Blume-Capel model with random crystal field interactions: An effective field theory analysis

TL;DR

This study analyzes the phase transitions and critical behavior of a spin-1 Blume-Capel model with random crystal fields on honeycomb and square lattices using an effective field theory approach, revealing complex phase diagrams and reentrant phenomena.

Contribution

It introduces an effective-field approximation that accounts for spin correlations in the Blume-Capel model with random crystal fields, providing detailed phase diagrams and identifying novel reentrant behaviors.

Findings

Phase diagrams with second and first order transitions and tricritical points.

Reentrant and double reentrant phenomena observed.

Effects of random crystal field parameters on phase behavior elucidated.

Abstract

A spin-1 Blume-Capel model with dilute and random crystal fields is examined for honeycomb and square lattices by introducing an effective-field approximation that takes into account the correlations between different spins that emerge when expanding the identities. For dilute crystal fields, we have given a detailed exploration of the global phase diagrams of the system in $k_{B}T_{c}/J-D/J$ plane with the second and first order transitions, as well as tricritical points. We have also investigated the effect of the random crystal field distribution characterized by two crystal field parameters $D/J$ and $\triangle/J$ on the phase diagrams of the system. The system exhibits clear distinctions in qualitative manner with coordination number $q$ for random crystal fields with $\triangle/J,D/J\neq0$. We have also found that, under certain conditions, the system may exhibit a number of interesting and unusual phenomena, such as reentrant behavior of first and second order, as well as a double reentrance with three successive phase transitions.