Critical and off‐critical singularities in disordered quantum magnets

Abstract

We study disordered systems at and near quantum phase transitions, which are transitions at zero temperature that are driven by quantum instead of thermal fluctuations. Special emphasis is put on the so‐called Griffiths‐McCoy regions surrounding these transitions in magnetic systems, where various susceptibilities are found to be divergent for T → 0 without the system being critical. We present a phenomenological picture for uncorrelated and weakly or strongly correlated disorder and check it for various models. In higher dimensions the phenomena seem to be connected to a percolation transition.