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

Cyclic Period-3 Window in Antiferromagnetic Potts and Ising Models on Recursive Lattices