The random field Blume-Capel model revisited

•We analyze the Blume Capel model in a random field and revisit the seminal work of Kaufman and Kanner.•The phase diagrams of the model are investigated when a random external field H is applied.•A classification of phase diagrams in terms of their topology is presented.•The effects of randomness on critical and multicritical phenomena are investigated. 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 (1990). 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. Although the phase diagrams exhibit a richness of multicritical phenomena we did not found any reentrant effect as have been seen in similar models.