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Abstract
This talk will discuss novel critical behavior and ``Griffiths-McCoy"
singularities (which occur away from criticality) near quantum phase
transitions in disordered systems with discrete (Ising) symmetry. One finds
that distributions of many quantities are very broad, so it is insufficient to
simply take the average. After reviewing some exact results in one-dimension
obtained using a real space renormalization group approach, I will discuss
extensions of these results obtained by a numerical method in which the spin
problem 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 dimensions,
at least for $d=2$.
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