Comparative study of the critical behavior in one-dimensional random and aperiodic environments

Details Comparative study of the critical behavior in one-dimensional random and aperiodic environments Comparative study of the critical behavior in one-dimensional random and aperiodic environments

1998-04-29

arxiv.org/abs/cond-mat/9804315v2

Europ. Phys. J. B 5, 613 (1998)

Physics

Condensed Matter

Statistical Mechanics

13 pages RevTeX, 10 eps-figures included

Scientific paper

10.1007/s100510050486

We consider cooperative processes (quantum spin chains and random walks) in one-dimensional fluctuating random and aperiodic environments characterized by fluctuating exponents omega>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 t ~ log^{1/omega}. Also some critical exponents, characterizing the singularities of average quantities, are found to be universal functions of omega, whereas some others do depend on details of the distribution of the disorder. In the off-critical region there is an important difference between the two types of environments: in aperiodic systems there are no extra (Griffiths)-singularities.

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