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

Róbert Juhász, Yu Cheng Lin, F. Iglói

Research output: Contribution to journalArticle

22 Citations (Scopus)

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 languageEnglish
Article number224206
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume73
Issue number22
DOIs
Publication statusPublished - 2006

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Distribution functions
Statistics
statistics
disorders
random numbers
exclusion
degrees of freedom
distribution functions
exponents
symmetry
excitation

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

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

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 73, No. 22, 224206, 2006.

Research output: Contribution to journalArticle

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