Abstract
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.
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