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The phase diagram of the mean-field Ising model in a random field obeying a symmetric threepeak distribution is determined. This distribution is relevant to diluted antiferromagnets in a uniform magnetic field. The phase diagram includes a fourth-order point, tricritical points, ordered critical points, critical end points, and a double critical end point. An ordered phase persists for arbitrarily large random fields at low temperatures.

The global phase diagram of the Blume-Capel model in a random field obeying the bimodal symmetric distribution is determined by using the mean-field method. The phase diagram includes an isolated ordered critical end point and two lines of tricritical points. A new phase emerges for strong enough random fields: the ferromagnetic-nonmagnetic phase. It is argued that such a phase occurs in three dimensions.