### Abstract

A decimation method is applied to the tight binding model describing the two-dimensional electron gas with next-nearest-neighbor interaction in the presence of an inverse golden mean magnetic flux. The critical phase with fractal spectrum and wave function exists in a finite window in two-dimensional parameter space introducing universal features. Our decimation scheme identifies nine quantitative universality classes characterized by the limit cycles of the decimation equations. The limit cycles describe the self-similarity of the wave functions and divide them into three broader qualitative classes where the wave functions are either symmetric, asymmetric, or exhibit a type of shifted symmetry. We conjecture that the rest of the critical phase, where the fractal wave functions do not exhibit self-similarity, is characterized by strange attractors of the renormalization equations. The results are compared with those of Han et al. [Phys. Rev. B 50, 11 365 (1994)] on the same model.

Original language | English |
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Pages (from-to) | 3026-3029 |

Number of pages | 4 |

Journal | Physical Review B |

Volume | 52 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1 Jan 1995 |

MoE publication type | Not Eligible |

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### Cite this

*Physical Review B*,

*52*(5), 3026-3029. https://doi.org/10.1103/PhysRevB.52.3026