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

TL;DR

This paper investigates the complex magnetic behaviors, including cyclic period-3 windows and chaos, in antiferromagnetic Potts and Ising models on recursive lattices using recurrence relations.

Contribution

It reveals the existence of cyclic period-3 windows and chaotic regimes in these models, expanding understanding of their phase dynamics on recursive lattices.

Findings

Identification of cyclic period-3 windows in the models

Calculation of Lyapunov exponents indicating chaos

Detection of modulated phases within the cyclic window

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.