  The magnetic properties of the antiferromagnetic Potts model with two-site
interaction and the antiferromagnetic Ising model with three-site interaction
on recursive lattices have been studied. A cyclic period-3 window has been
revealed by the recurrence relation method in the antiferromagnetic Q-state
Potts model on the Bethe lattice (at Q<2) and in the antiferromagnetic Ising
model with three-site interaction on the Husimi cactus. The Lyapunov exponents
have been calculated, modulated phases and a chaotic regime in the cyclic
period-3 window have been found for one-dimensional rational mappings
determined the properties of these systems.
