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

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 .

Spin-1 Ising/Ising-Heisenberg CPPT 2017 Yerevan diamond chain diamond-like decorated Bethe lattice for q=3

Hamiltonian CPPT 2017 Yerevan

Dynamical approach CPPT 2017 Yerevan

Recurrence relation CPPT 2017 Yerevan

parameters CPPT 2017 Yerevan

magnetic and quadrupole moments CPPT 2017 Yerevan

Lyapunov exponents Zero - dynamic counterpart of a CPPT 2017 Yerevan Positive - chaotic, unstable states, Zero - dynamic counterpart of a second-order phase transition Negative - stable states

Lyapunov exponents for 1D maps CPPT 2017 Yerevan 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

Lyapunov exponents for 2D maps CPPT 2017 Yerevan

CPPT 2017 Yerevan Magnetization

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CPPT 2017 Yerevan Lyampunov exponents

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