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.