# The random field Blume-Capel model revisited

## TL;DR

This paper revisits the mean-field analysis of the Blume-Capel model with a random magnetic field, exploring how the phase diagram structures change with randomness, and finds no reentrant phenomena despite rich multicritical behavior.

## Contribution

It provides a detailed classification of phase diagram topologies in the random field Blume-Capel model, extending previous work and analyzing the effects of randomness on phase structures.

## Key findings

- Phase diagrams classified into five topologies.
- Phase diagram topology remains consistent across H-T and D-T planes.
- No reentrant phenomena observed despite multicritical richness.

## Abstract

We have revisited the mean-field treatment for the Blume-Capel model under the presence of a discrete random magnetic field as introduced by Kaufman and Kanner. The magnetic field ($H$) versus temperature ($T$) phase diagrams for given values of the crystal field $D$ were recovered in accordance to Kaufman and Kanner original work. However, our main goal in the present work was to investigate the distinct structures of the crystal field versus temperature phase diagrams as the random magnetic field is varied because similar models have presented reentrant phenomenon due to randomness. Following previous works we have classified the distinct phase diagrams according to five different topologies. The topological structure of the phase diagrams is maintained for both $H-T$ and $D-T$ cases. Althoug the phase diagrams exhibit a richness of multicritical phenomena we did not found any reentrant effect as have been seen in similar models.