### Abstract

The effect of quenched disorder on the low-energy and low-temperature properties of various two-and three-dimensional Heisenberg models is studied by a numerical strong disorder renormalization-group method. For strong enough disorder we have identified two relevant fixed points, in which the gap exponent, ω, describing the low-energy tail of the gap distribution P(Δ)∼Δ^{ω} is independent of disorder, the strength of couplings, and the value of the spin. The dynamical behavior of nonfrustrated random antiferromagnetic models is controlled by a singletlike fixed point, whereas for frustrated models the fixed point corresponds to a large spin formation and the gap exponent is given by ω≈0. Another type of universality class is observed at quantum critical points and in dimerized phases but no infinite randomness behavior is found, in contrast to that of one-dimensional models.

Original language | English |
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Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 68 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 1 2003 |

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

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## Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*68*(2). https://doi.org/10.1103/PhysRevB.68.024424