Eur. Phys. J. B 1, 513-517 (1998)
https://doi.org/10.1007/s100510050213

Random and aperiodic quantum spin chains: A comparative study

¹ Research Institute for Solid State Physics, 1525 Budapest, P.O.Box 49, Hungary
² Laboratoire de Physique des Matériaux, Université Henri Poincaré, 54506 Vandœuvre-les-Nancy, France
³ HLRZ, Forschungszentrum Jülich, 52425 Jülich, Germany

Corresponding author: ^a heiko@hlrz.kfa-juelich.de

Received: 18 November 1997
Revised: 24 November 1997
Accepted: 8 January 1997
Published online: 15 February 1998

Abstract

According to the Harris-Luck criterion the relevance of a fluctuating interaction at the critical point is connected to the value of the fluctuation exponent ω. Here we consider different types of relevant fluctuations in the quantum Ising chain and investigate the universality class of random as well as deterministic-aperiodic models. At the critical point the random and aperiodic systems behave similarly, due to the same type of extreme broad distribution of the energy scales at low energies. The critical exponents of some averaged quantities are found to be a universal function of ω, but some others do depend on other parameters of the distribution of the couplings. In the off-critical region there is an important difference between the two systems: there are no Griffiths singularities in aperiodic models.