2006/02/03 by Robert Juhasz, Róbert Juhász, Yu-Cheng Lin +3 · 1 citation
Mathematics · Physics and Astronomy · #Degrees of freedom (physics and chemistry) #Distribution (mathematics) #Exponent #Extreme value theory #Gravitational singularity #Independent and identically distributed random variables #Inverse #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Random variable #Renormalization group #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.1103/physrevb.73.224206
11 pages, 11 figures
arxiv created 2006/02/03 · openalex publication_date 2006/06/21 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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, \ensuremathτ^\ensuremath-1, in finite samples of linear size, L, either exactly or numerically. In all cases, having a discrete symmetry, the distribution function, P(\ensuremathτ^\ensuremath-1,L), is found to depend on the variable, u=\ensuremathτ^\ensuremath-1Lz, 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 Fr'echet distribution of P(\ensuremathτ^\ensuremath-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.