Global mean-field phase diagram of the spin-1 Ising ferromagnet in a random crystal field

We study the phase diagram of the mean-field spin-1 Ising ferromagnet in a uniform magnetic field H and a random crystal field Δi, with probability distribution P(Δi) = pδ(Δi −Δ) + (1 − p)δ(Δi). We analyse the effects of randomness on the first-order surfaces of the Δ−T−H phase diagram for different values of the concentration p and show how these surfaces are affected by the dilution of the crystal field.