Superstable cycles and magnetization plateaus for antiferromagnetic spin-1 Ising and Ising-Heisenberg models on diamond chains

We consider the appearance of superstable cycles in the dynamical approach to the antiferromagnetic and ferromagnetic spin-1 Ising and Ising-Heisenberg models on diamond chains, and their connection with magnetization plateaus. The rational mappings, which provide the statistical properties of the model, are derived by using recurrence relations technique. We consider stability properties of the mapping, providing evidences of a connection between magnetization plateaus and dynamical properties, as the behavior of Lyapunov exponents. The newfound correspondence between superstable point and zero magnetic plateau in spin-1 models on a diamond chain has been tested for a range of parameters.