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

Ananikian, N. S.; Artuso, Roberto; Poghosyan, Hasmik

doi:10.1016/j.physa.2018.03.023

Cited by 3 publications

(2 citation statements)

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“…There are many methods for defining the partition function [15]. We are considering the recursive relations method [16,17]. In this method the lattice is cut into branches and the total partition function is expressed in terms of the reduced partition functions of all branches (see Figure 2).…”

Section: Partition Functionmentioning

confidence: 99%

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Magnetization properties, super-stable points, and cycles of antiferromagnetic spin-1 diamond chains with nodal-nodal interactions

Amatuni,

Burdik,

Poghosyan

et al. 2023

J. Phys.: Conf. Ser.

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This study is devoted to the discovery of super-stable points and cycles in antiferromagnetic Ising and Ising-Heisenberg models with spin 1 on diamond chains with nodal-nodal interactions. These phenomena are important for understanding the complex behavior of magnetic systems. We specifically investigate their connection with magnetization plateaus, which serve as critical indicators of the model’s characteristics. Employing the recurrence relations technique, we derive multidimensional rational mappings that give insights about the statistical properties of the models. Carefully examining the stability properties of these mappings, in particular, by analyzing the maximum Lyapunov exponent, we have revealed the complex relationship between the magnetization plateau and dynamic properties. Throughout our extensive research, we have comprehensively studied the existence and behavior of super-stable points and cycles for various parameter configurations in spin-1 models on the diamond chains. By highlighting the basic properties of dynamics and stability, our research advances a fundamental understanding of complex magnetic systems and their fascinating properties.

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Section: Partition Functionmentioning

confidence: 99%

“…Such exponents are computed from dynamical recursion equations: a zero maximum Lyapunov exponents is the dynamic counterpart of a second-order phase transition. If we have a dimensional map then a spectrum of exponents is present [6,13,15,16]; the Lyapunov exponent is calculated by the following equation:…”

Section: Partition Functionmentioning

confidence: 99%