Ising spin system on the Fibonacci chain

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Abstract
A study of the ground-state and thermodynamic properties of the Ising spin system was carried out including an external magnetic field where two exchange energies are arranged according to a Fibonacci sequence. For this model, the decimation renormalization transformation can be performed exactly as shown recently by Achiam, Lubensky, and Marshall. It is found that there is a new fixed plane of two-cycle limit points. Using the recursion relation of the free energy, we calculate numerically the physical quantities when the two exchange energies have opposite signs. It is shown that the chain becomes magnetized stepwise by the external field and that the magnetic susceptibility and the specific heat oscillate as a function of the temperature. These characteristic features can be understood, based on the hierarchical cluster structure of the ground state.

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