Statistical Physics Group

We study the critical behavior of Ising quantum magnets with broadly distributed random couplings (J), such that P(In J) â^Œ |ln J|-1-α, α > 1, for large |ln J| (LeÌ�vy flight statistics). For sufficiently broad distributions, α < αc, the critical behavior is controlled by a line of fixed points, where the critical exponents vary with the LeÌ�vy index, α. In one dimension, with αc = 2, we obtained 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 αc âo/oo^ 4.5. Thus in the region 2 < α < αc, where the central limit theorem holds for |ln J| the broadness of the distribution is relevant for the 2d quantum Ising model.