One-dimensional mapping, modulated phases and Lyapunov exponent for the antiferromagnetic \(Q\)-state Potts and multi-site exchange interaction Ising models
The authors describe the bifurcation structure, period doubling and chaos for the antiferromagnetic \(Q\)-state Potts model on the Bethe lattice and three-site interaction Ising model on Husimi one in a magnetic field, by using the recursion relation technique. A chaotic behavior of the magnetic susceptibility for the models is observed at low temperatures. The resulting one-dimensional rational mapping has a positive Lyapunov exponent in the region of the chaotic regime for the antiferromagnetic \(Q\)-state Potts \((Q<2)\) and three-site interaction Ising models. They also discuss modulated phases for the antiferromagnetic \(Q\)-state Potts (\(Q<2\) and \(Q\geq 2\)) and three-site interaction Ising model. At low temperatures the \(Q\)-state Potts model (\(Q\geq 2\)) has only one modulated phase with \(\frac 12\) pinching corresponding to the 2-cycle. The \(Q\)-state Potts \((Q<2)\) and three-site interaction Ising models have an infinite number of modulated phases with different pinching numbers and the authors construct the first modulated phase after the first bifurcation point.
scientific article; zbMATH DE number 5791161