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The European Physical Journal B
ISSN: 1434-6028 (printed version)
ISSN: 1434-6036 (electronic version)
Abstract Volume 5 Issue 3 (1998) pp 613-625
Comparative study of the critical behavior in one-dimensional random and aperiodic environments
F. Iglói (1)(4) (a), D. Karevski (2), H. Rieger (3)(4)
(1) Research Institute for Solid State Physics, 1525 Budapest, P.O.Box 49, Hungary
(2) Laboratoire de Physique des Materiaux, Université Henri Poincaré, 54506 Vanduvre les Nancy, France
(3) Institut für Theoretische Physik, Universität zu Köln, 50923 Köln, Germany
(4) HLRZ, Forschungszentrum Jülich, 52425 Jülich, Germany
Received: 5 February 1998 / Accepted: 17 April 1998
Abstract: We consider cooperative processes (quantum spin chains and random walks) in one-dimensional fluctuating random and aperiodic environments characterized by fluctuating exponents $\omega\gt$. 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 $L\sim(\ln t)^{1/\omega}$. 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.
PACS. 05.50.+q Lattice theory and statistics; Ising problems - 64.60.Ak Renormalization-group, fractal, and percolation studies of phase transitions - 68.35.Rh Phase transitions and critical phenomena
(a) Permanent address: Institute for Theoretical Physics, Szeged University, 6720 Szeged, Hungary. email: h.rieger@fz-juelich.de or email: rieger@thp.uni-koeln.de
Article in PDF format (505 KB)
Online publication: October 26, 1998
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