Comparative Study of the Critical Behavior in One-Dimensional Random and Aperiodic Environments

Ferenc Iglói, Dragi Karevski, Heiko Rieger

Published Jan 1, 1998• 12 citations

Abstract

We consider cooperative processes (quantum spin chains and random walks) in one-dimensional fluctuating random and aperiodic environments characterized by fluctuating exponents #>0. At the critical point the random and aperiodic systems scale essentially anisotropically in a similar fashion: length (L) and time (t) scales are related as L # (ln t) 1/# . Also some critical exponents, characterizing the singularities of average quantities, are found to be universal functions of #, whereas some others do depend on details of the distribution of the disorder. In the off-critical region there is an important di#erence between the two types of environments: in aperiodic systems there are no extra (Griffiths)-singularities.

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