1. Hayk Poghosyan A.I. Alikhanyan National Science Laboratory, Armenia
Dynamical system approach and super-stable  points  for antiferromagnetic spin-1 Ising-Heisenberg models on diamond chain and  diamond-like decorated Bethe lattices.
Hayk Poghosyan
A.I. Alikhanyan National Science Laboratory, Armenia

2. CPPT 2017 Yerevan
Dynamical systems
The theory of dynamical systems, besides its intrinsic theoretical relevance, recently had a significant impact on a wide range of disciplines from physics to ecology and economics, providing methodological tools which are currently employed in financial and economic forecasting, environmental modelling, medical diagnosis, industrial equipment diagnosis etc [Guckenheimer, Oster, Ipaktchi, J. of Math. Biology 4 (1977); Brianzoni, Michetti, Sushko . Math. and Computers in Simulation 81 (2010); Miskiewicz, Ausloos, Physica A 336 (2004) ].
We use dynamical techniques in the analysis of Ising and Ising-Heisenberg spin models on a diamond chain and diamond-like decorated Bethe lattices .

3. Spin-1 Ising/Ising-Heisenberg
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diamond chain
diamond-like decorated
Bethe lattice for q=3

4. Hamiltonian
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5. Dynamical approach
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6. Recurrence relation
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7. parameters
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8. magnetic and quadrupole moments
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9. Lyapunov exponents Zero - dynamic counterpart of a
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Positive - chaotic, unstable states,
Zero dynamic counterpart of a
second-order phase transition
Negative - stable states

10. Lyapunov exponents for 1D maps
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Lyapunov exponents for 1D maps
We choose an initial point and let the map iterate this for say n times. We denote it
Calculate
The lyapunov exponent will be equal to

11. Lyapunov exponents for 2D maps
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12. CPPT 2017 Yerevan
Magnetization

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Quadrupole moment

14. CPPT 2017 Yerevan
Lyampunov exponents

15. CPPT 2017 Yerevan

16. CPPT 2017 Yerevan
Thank You!