### Abstract

We consider interacting many-particle systems with quenched disorder having strong Griffiths singularities, which are characterized by the dynamical exponent, z, such as random quantum systems and exclusion processes. In several d=1 and d=2 dimensional problems we have calculated the inverse time scales, τ-1, in finite samples of linear size, L, either exactly or numerically. In all cases, having a discrete symmetry, the distribution function, P (τ-1, L), is found to depend on the variable, u= τ-1 Lz, and to be universal given by the limit distribution of extremes of independent and identically distributed random numbers. This finding is explained in the framework of a strong disorder renormalization group approach when, after fast degrees of freedom are decimated out, the system is transformed into a set of noninteracting localized excitations. The Fréchet distribution of P (τ-1, L) is expected to hold for all random systems having a strong disorder fixed point, in which the Griffiths singularities are dominated by disorder fluctuations.

Original language | English |
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Article number | 224206 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 73 |

Issue number | 22 |

DOIs | |

Publication status | Published - 2006 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

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

*73*(22), [224206]. https://doi.org/10.1103/PhysRevB.73.224206

**Strong Griffiths singularities in random systems and their relation to extreme value statistics.** / Juhász, Róbert; Lin, Yu Cheng; Iglói, F.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 73, no. 22, 224206. https://doi.org/10.1103/PhysRevB.73.224206

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TY - JOUR

T1 - Strong Griffiths singularities in random systems and their relation to extreme value statistics

AU - Juhász, Róbert

AU - Lin, Yu Cheng

AU - Iglói, F.

PY - 2006

Y1 - 2006

N2 - We consider interacting many-particle systems with quenched disorder having strong Griffiths singularities, which are characterized by the dynamical exponent, z, such as random quantum systems and exclusion processes. In several d=1 and d=2 dimensional problems we have calculated the inverse time scales, τ-1, in finite samples of linear size, L, either exactly or numerically. In all cases, having a discrete symmetry, the distribution function, P (τ-1, L), is found to depend on the variable, u= τ-1 Lz, and to be universal given by the limit distribution of extremes of independent and identically distributed random numbers. This finding is explained in the framework of a strong disorder renormalization group approach when, after fast degrees of freedom are decimated out, the system is transformed into a set of noninteracting localized excitations. The Fréchet distribution of P (τ-1, L) is expected to hold for all random systems having a strong disorder fixed point, in which the Griffiths singularities are dominated by disorder fluctuations.

AB - We consider interacting many-particle systems with quenched disorder having strong Griffiths singularities, which are characterized by the dynamical exponent, z, such as random quantum systems and exclusion processes. In several d=1 and d=2 dimensional problems we have calculated the inverse time scales, τ-1, in finite samples of linear size, L, either exactly or numerically. In all cases, having a discrete symmetry, the distribution function, P (τ-1, L), is found to depend on the variable, u= τ-1 Lz, and to be universal given by the limit distribution of extremes of independent and identically distributed random numbers. This finding is explained in the framework of a strong disorder renormalization group approach when, after fast degrees of freedom are decimated out, the system is transformed into a set of noninteracting localized excitations. The Fréchet distribution of P (τ-1, L) is expected to hold for all random systems having a strong disorder fixed point, in which the Griffiths singularities are dominated by disorder fluctuations.

UR - http://www.scopus.com/inward/record.url?scp=33745673149&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33745673149&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.73.224206

DO - 10.1103/PhysRevB.73.224206

M3 - Article

AN - SCOPUS:33745673149

VL - 73

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 22

M1 - 224206

ER -