  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 omega. Here we consider different types of relevant fluctuations in
the quantum Ising chain and investigate the universality class of the 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 omega, 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.
