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Journal of Physics Conference Series

Super-stable points and cycles on double-tetrahedral chains

Gayane A. Amatuni, Č. Burdík, Hasmik Poghosyan, L. Ananikyan, N.S. Ananikian

Published Dec 1, 2024• 0 citations
Publisher

Abstract

Abstract Quantum systems with antiferromagnetic spin-1 Ising and Ising-Heisenberg interactions with single-ion anisotropy on double-tetrahedral chains can exhibit unconventional classical and quantum states responsible for the anomalous behavior of magnetization curves at low temperatures. We find super-stable points and cycles for those chains when the temperature tends to zero.

DOI
10.1088/1742-6596/2912/1/012038

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Abstract We study spin-1 antiferromagnetic Ising–Heisenberg models on diamond chains with biquadratic nodal–nodal interactions, focusing on the emergence of superstable points and cycles. Using recurrence relations to derive multidimensional rational mappings, we analyze their stability via the maximum Lyapunov exponent. This reveals a clear link between dynamical features and magnetization plateaus. Our results highlight how super-stable behavior reflects key aspects of the system’s magnetic and dynamic properties across various parameter regimes.
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The zero-temperature phase diagram of the anisotropic, strongly disordered antiferromagnetic quantum spin-1 chain is investigated, within the framework of a real-space renormalization-group approach. In the presence of uniform anisotropy there occurs a phase transition from a random singlet phase to an Ising antiferromagnetic phase controlled by a fixed point that does not have Heisenberg symmetry. We find evidence of a fixed point due to randomness in the anisotropy similar to that which occurs for quantum Heisenberg spin-12\frac{1}{2}21​ chains.
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