Eur. Phys. J. B 5, 613-625 (1998)
https://doi.org/10.1007/s100510050486

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

¹ Research Institute for Solid State Physics, 1525 Budapest, P.O.Box 49, Hungary
² HLRZ, Forschungszentrum Jülich, 52425 Jülich, Germany
³ Laboratoire de Physique des Materiaux, Université Henri Poincaré, 54506 Vandœuvre les Nancy, France
⁴ Institut für Theoretische Physik, Universität zu Köln, 50923 Köln, Germany

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Received: 5 February 1998
Accepted: 17 April 1998
Published online: 15 October 1998

Abstract

We consider cooperative processes (quantum spin chains and random walks) in one-dimensional fluctuating random and aperiodic environments characterized by fluctuating exponents . 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 . Also some critical exponents, characterizing the singularities of average quantities, are found to be universal functions of ω, 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.