One-dimensional mapping, modulated phases and Lyapunov exponent for the antiferromagnetic \(Q\)-state Potts and multi-site exchange interaction Ising models
type: Item
instance of: scholarly article
title: One-dimensional mapping, modulated phases and Lyapunov exponent for the antiferromagnetic \(Q\)-state Potts and multi-site exchange interaction Ising models
zbMATH Open document ID: 1211.37096
author: N. Ananikian
author: L. Ananikyan
author: V. V. Hovhannisyan
author: R. Artuso
published in: Physica D
publication date: 2010-09-24T00:00:00Z
review text: 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.
reviewed by: Xingfu Zou
Mathematics Subject Classification ID: 37N20
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 82B20
Mathematics Subject Classification ID: 82D40
Mathematics Subject Classification ID: 82B26
zbMATH DE Number: 5791161
zbMATH Keywords: lattice theory
zbMATH Keywords: classical spin models
zbMATH Keywords: antiferromagnetics
zbMATH Keywords: nonlinear dynamics and chaos
zbMATH Keywords: Lyapunov exponent
MaRDI profile type: Publication
full work available at URL: j.physd.2010.05.007
OpenAlex ID: W2016340817
cites work: Chaotic repellers in the antiferromagnetic Ising model
cites work: Correlation inequalities on some partially ordered sets
cites work: Abelian sandpile model on the Husimi lattice of square plaquettes
cites work: Small denominators. I. Mappings of the circumference onto itself
cites work: Q4266365
cites work: Analytical study of the superstable 3-cycle in the logistic map
cites work: Products of random matrices in statistical physics
DOI: 10.1016/J.PHYSD.2010.05.007
description: scientific article; zbMATH DE number 5791161