Quantum phase transitions in random magnets

This talk will discuss novel critical behavior and "Griffiths-McCoy" singul arities (which occur away from criticality) near quantum phase transitions in disordered systems with discrete (Ising) symmetry. One finds that distri butions of many quantities are very broad. so it is insufficient to simply take the average. After reviewing some exact results in one dimension obtai ned using a real space renormalization group approach, I will discuss exten sions of these results obtained by a numerical method in which the spin pro blem is mapped on to free fermions. In this way, whole distributions can be determined with precision. The talk will then describe quantum Monte Carlo simulations which show that similar results also occur in higher dimension s, at least for d = 2. (C) 2001 Elsevier Science B.V. All rights reserved.