Exact solution of the one-dimensional J2 model of superconducting networks in a magnetic field
R. B. Griffiths, L. M. Floría
DOI 10.1103/PhysRevB.45.9887 · Physical Review B
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Abstract
A simplified one-dimensional model of certain nonperiodic networks of superconducting wires in a magnetic field, introduced by Grest, Chaikin, and Levine, is solved exactly by reducing it to a mathematical problem involving Fourier transforms of one-dimensional sequences. Explicit results are obtained for some particular cases including that of the ‘‘Fibonacci sequence’’ considered by them. Inflation symmetry appears to play no significant role; the crucial question is the existence and structure of a discrete spectrum in the Fourier transform.
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