Random quantum magnets with broad disorder distribution

We study the critical behavior of Ising quantum magnets with broadly distri buted random couplings (J), such that P(ln J) similar to \ In J \ (-1-alpha ), alpha > 1, for large \ In J \ (Levy flight statistics). For sufficiently broad distributions, alpha < <alpha>(e), the critical behavior is controll ed by a line of fixed points, where tile critical exponents var!: with tile Levy index, alpha. In one! dimension, with alpha (c) = 2, we obtained seve ral exact results through a mapping to surviving Riemann walks. In two dime nsions the varying critical exponents have been calculated by a numerical i mplementation of the Ma-Dasgupta-Hu renormalization group method leading to alpha (c) approximate to 4.5. Thus in tile region 2 < <alpha> < <alpha>(c) , where the central limit theorem holds fur \ In J \ the broadness of the d istribution is relevant for the 2d quantum Ising model.