Mean-field solution of the Blume–Capel model under a random crystal field

•We introduce a disordered exactly soluble version of the Blume–Capel model with infinite-range interactions.•The disorder is represented by quenched random crystal field anisotropy.•A classification of phase diagrams in terms of their topology is presented.•The effects of randomness on critical and multicritical phenomena are investigated.

In this work we investigate the Blume–Capel model with infinite-range ferromagnetic interactions and under the influence of a quenched disorder – a random crystal field. For a suitable choice of the random crystal field the model displays a wealth of multicritical behavior, continuous and first-order transition lines, as well as re-entrant behavior. The resulting phase diagrams show a variety of topologies as a function of the disorder parameter p. A comparison with recent results on the Blume–Capel model in random crystal field is discussed.