  We study the critical behavior of Ising quantum magnets with broadly
distributed random couplings (J), such that $P(\ln J) \sim |\ln
J|^{-1-\alpha}$, $\alpha>1$, for large $|\ln J|$ (L\'evy flight statistics).
For sufficiently broad distributions, $\alpha<\alpha_c$, the critical behavior
is controlled by a line of fixed points, where the critical exponents vary with
the L\'evy index, $\alpha$. In one dimension, with $\alpha_c=2$, we obtaind
several exact results through a mapping to surviving Riemann walks. In two
dimensions the varying critical exponents have been calculated by a numerical
implementation of the Ma-Dasgupta-Hu renormalization group method leading to
$\alpha_c \approx 4.5$. Thus in the region $2<\alpha<\alpha_c$, where the
central limit theorem holds for $|\ln J|$ the broadness of the distribution is
relevant for the 2d quantum Ising model.
