Random quantum magnets with broad disorder distribution

We study the critical behavior of Ising quantum magnets with broadly distributed random couplings (J), such that $P(\ln J) \sim |\ln J|^{-1-\alpha}$,$\alpha>1$,forlarge$|\ln J|$ (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 $\mathrm{\mid }\ln J\mathrm{\mid }$ the broadness of the distribution is relevant for the 2d quantum Ising model.