  We use a simple lattice statistical model to analyze the effects of
directional interactions on the phase diagram of a fluid of two-state Janus
particles. The problem is formulated in terms of nonlinear recursion relations
along the branches of a Cayley tree. Directional interactions are taken into
account by the geometry of this graph. Physical solutions on the Bethe lattice
(the deep interior of a Cayley tree) come from the analysis of the attractors
of the recursion relations. We investigate a number of situations, depending on
the concentrations of the types of Janus particles and the parameters of the
potential, and make contact with results from recent numerical simulations.
