  A four-state clock ferromagnetic model is studied in the presence of
different configurations of anisotropies and random fields. The model is
considered in the limit of infinite-range interactions, for which the
mean-field approach becomes exact. Both representations of Cartesian spin
components and two Ising variables are used, in terms of which the physical
properties and phase diagrams are discussed. The random fields follow bimodal
probability distributions and the richest criticality is found when the fields,
applied in the two Ising systems, are not correlated. The phase diagrams
present new interesting topologies, with a wide variety of critical
points,which are expected to be useful in describing different complex
phenomena.
