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      Chaotic Spin Correlations in Frustrated Ising Hierarchical Lattices

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          Abstract

          Spin-spin correlations are calculated in frustrated hierarchical Ising models that exhibit chaotic renormalization-group behavior. The spin-spin correlations, as a function of distance, behave chaotically. The far correlations, but not the near correlations, are sensitive to small changes in temperature or frustration, with temperature changes having a larger effect. On the other hand, the calculated free energy, internal energy, and entropy are smooth functions of temperature. The recursion-matrix calculation of thermodynamic densities in a chaotic band is demonstrated. The leading Lyapunov exponents are calculated as a function of frustration.

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          Spin-Glass Behavior in Frustrated Ising Models with Chaotic Renormalization-Group Trajectories

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            Recursive weighted treelike networks

            We propose a geometric growth model for weighted scale-free networks, which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks, which are partially determined by the parameters. Analytical results indicate that the resulting networks have power-law distributions of degree, strength, weight and betweenness, a scale-free behavior for degree correlations, logarithmic small average path length and diameter with network size. The obtained properties are in agreement with empirical data observed in many real-life networks, which shows that the presented model may provide valuable insight into the real systems.
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              Publisher's Note: Griffiths singularities and algebraic order in the exact solution of an Ising model on a fractal modular network [Phys. Rev. E75, 061104 (2007)]

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                Author and article information

                Journal
                10.1103/PhysRevB.79.014434
                0810.4586

                Condensed matter,Theoretical physics
                Condensed matter, Theoretical physics

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