Quasiperiodic anisotropicXYmodel

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Abstract
The quasiperiodic anisotropic XY model in one-dimensional exhibits ordered and disordered phases with cantor spectra which we characterize in terms of the exponent δ and the f(α) curve. The transition to the long-range-order phase is signaled by a nonanalyticity in δ in addition to the singular behavior of the long-range correlation function. Based on our numerical results, we conjecture that f(α) is a smooth function in the disordered phase, becoming discontinuous in the ordered phase. At a special point in the ordered phase, the system exhibits a pointlike spectrum with localized states.