The effect of quenched disorder is often relevant, as far as the long-time, long-distance behavior of many particle systems is considered. For relevant perturbations disorder and deterministic fluctuations are usually in the same order of magnitude and the random fixed point is conventional. There is, however, a class of problems for which the singular behavior is controlled by a strong disorder fixed point, in which disorder grows without limit during renormalization. This type of behavior is first studied in random quantum spin chains, but recently strong disorder fixed points have been observed in classical systems, such as in the random bond Potts model in the large-q limit and in nonequilibrium processes, such as in absorbing state phase transitions and in driven lattice gas models. In this talk we review these latter developments, in particular we show how the critical singularities of the different problems, which are related to each other, can be exactly calculated. We also mention results about the Griffiths phases and higher dimensional problems.

Research Institute for Solid State Physics and Optics and Institute of Theoretical Physics, Hungary