### Abstract

We study the critical behavior of Ising quantum magnets with broadly distributed random couplings (J), such that P(In J) ∼ |ln J|^{-1-α}, α > 1, for large |ln J| (Lévy flight statistics). For sufficiently broad distributions, α < α_{c}, the critical behavior is controlled by a line of fixed points, where the critical exponents vary with the Lévy index, α. In one dimension, with α_{c} = 2, we obtained several exact results through a mapping to surviving Riemann walks. In two dimensions the varying critical exponents have been calculated by a numerical implementation of the Ma-Dasgupta-Hu renormalization group method leading to α_{c} ≈ 4.5. Thus in the region 2 < α < α_{c}, where the central limit theorem holds for |ln J| the broadness of the distribution is relevant for the 2d quantum Ising model.

Original language | English |
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Pages (from-to) | 267-276 |

Number of pages | 10 |

Journal | European Physical Journal B |

Volume | 20 |

Issue number | 2 |

DOIs | |

Publication status | Published - Mar 2 2001 |

### Keywords

- 05.30.Ch Quantum ensemble theory
- 75.10.Nr Spin-glass and other random models
- 75.40.Gb Dynamic properties (dynamic susceptibility, spin waves, spin diffusion, dynamic scaling, etc.)
- 75.50.Lk Spin glasses and other random magnets

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

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## Cite this

*European Physical Journal B*,

*20*(2), 267-276. https://doi.org/10.1007/PL00011100