RANDOM AND APERIODIC QUANTUM SPIN CHAINS - A COMPARATIVE-STUDY

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