### Abstract

We study the phase diagram of the tight-binding model for an electron on an anisotropic square lattice with a four-dimensional parameter space defined by two nearest-neighbour and two next-nearest-neighbour couplings. Using a renormalization scheme, we show that the inequality of the two next-nearest-neighbour couplings destroys the fat critical regime found in the isotropic case above the bicritical line and replaces it with another re-entrant extended phase. The scaling properties of the model are those of the corresponding tight-binding models on the nearest-neighbour square and triangular lattices. The triangular universality class also describes the quantum Ising chain in a transverse field with the only exception being the conformally invariant state of the Ising model which has no analogue in the triangular-lattice case.

Original language | English |
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Pages (from-to) | 1123-1132 |

Number of pages | 10 |

Journal | Journal of Physics Condensed Matter |

Volume | 9 |

Issue number | 5 |

DOIs | |

Publication status | Published - 3 Feb 1997 |

MoE publication type | Not Eligible |

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### Cite this

*Journal of Physics Condensed Matter*,

*9*(5), 1123-1132. https://doi.org/10.1088/0953-8984/9/5/016

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*Journal of Physics Condensed Matter*, vol. 9, no. 5, pp. 1123-1132. https://doi.org/10.1088/0953-8984/9/5/016

**The re-entrant phase diagram of the generalized Harper equation.** / Ketoja, Jukka A.; Satija, Indubala I.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - The re-entrant phase diagram of the generalized Harper equation

AU - Ketoja, Jukka A.

AU - Satija, Indubala I.

PY - 1997/2/3

Y1 - 1997/2/3

N2 - We study the phase diagram of the tight-binding model for an electron on an anisotropic square lattice with a four-dimensional parameter space defined by two nearest-neighbour and two next-nearest-neighbour couplings. Using a renormalization scheme, we show that the inequality of the two next-nearest-neighbour couplings destroys the fat critical regime found in the isotropic case above the bicritical line and replaces it with another re-entrant extended phase. The scaling properties of the model are those of the corresponding tight-binding models on the nearest-neighbour square and triangular lattices. The triangular universality class also describes the quantum Ising chain in a transverse field with the only exception being the conformally invariant state of the Ising model which has no analogue in the triangular-lattice case.

AB - We study the phase diagram of the tight-binding model for an electron on an anisotropic square lattice with a four-dimensional parameter space defined by two nearest-neighbour and two next-nearest-neighbour couplings. Using a renormalization scheme, we show that the inequality of the two next-nearest-neighbour couplings destroys the fat critical regime found in the isotropic case above the bicritical line and replaces it with another re-entrant extended phase. The scaling properties of the model are those of the corresponding tight-binding models on the nearest-neighbour square and triangular lattices. The triangular universality class also describes the quantum Ising chain in a transverse field with the only exception being the conformally invariant state of the Ising model which has no analogue in the triangular-lattice case.

UR - http://www.scopus.com/inward/record.url?scp=5644250826&partnerID=8YFLogxK

U2 - 10.1088/0953-8984/9/5/016

DO - 10.1088/0953-8984/9/5/016

M3 - Article

AN - SCOPUS:5644250826

VL - 9

SP - 1123

EP - 1132

JO - Journal of Physics: Condensed Matter

JF - Journal of Physics: Condensed Matter

SN - 0953-8984

IS - 5

ER -