Superstable cycles for antiferromagnetic Q-state Potts and three-site interaction Ising models on recursive lattices
arXiv:1307.6038 · doi:10.1016/j.cnsns.2014.03.009
Abstract
We consider the superstable cycles of the Q-state Potts (QSP) and the three-site interaction antiferromagnetic Ising (TSAI) models on recursive lattices. The rational mappings describing the models' statistical properties are obtained via the recurrence relation technique. We provide analytical solutions for the superstable cycles of the second order for both models. A particular attention is devoted to the period three window. Here we present an exact result for the third order superstable orbit for the QSP and a numerical solution for the TSAI model. Additionally, we point out a non-trivial connection between bifurcations and superstability: in some regions of parameters a superstable cycle is not followed by a doubling bifurcation. Furthermore, we use symbolic dynamics to understand the changes taking place at points of superstability and to distinguish areas between two consecutive superstable orbits.
12 pages, 5 figures. Updated version for publication
References in corpus (8)
- Ordered states of adatoms on graphene
- The lengths distribution of laminar phases for type-I intermittency in the presence of noise
- Magnetic properties, Lyapunov exponent and superstability of the spin-1/2 Ising-Heisenberg model on diamond chain
- Phase Transition of the Ising model on a Hyperbolic Lattice
- Quantum melting of charge ice and non-Fermi-liquid behavior: An exact solution for the extended Falicov-Kimball model in the ice-rule limit
- The Spin Glass Phase in the Four-State, Three-Dimensional Potts Model
- Cyclic Period-3 Window in Antiferromagnetic Potts and Ising Models on Recursive Lattices
- Arnold Tongues and Feigenbaum Exponents of the Rational Mapping for Q-state Potts Model on Recursive Lattice: Q<2