Articles in peer-reviewed journals
|Random quantum magnets with broad disorder distribution|
|Karevski D., Lin Y.-C., Rieger H., Kawashima N., Iglói F.|
|European Physical Journal B 20 (2001) 267|
|ArXiv : cond-mat/0009144 [PDF]|
We study the critical behavior of Ising quantum magnets with broadly distributed random couplings (J), such that P(In J) â^¼ |ln J|-1-Î±, Î± > 1, for large |ln J| (LeÌ�vy flight statistics). For sufficiently broad distributions, Î± < Î±c, the critical behavior is controlled by a line of fixed points, where the critical exponents vary with the LeÌ�vy index, Î±. In one dimension, with Î±c = 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 Î±c âo/oo^ 4.5. Thus in the region 2 < Î± < Î±c, where the central limit theorem holds for |ln J| the broadness of the distribution is relevant for the 2d quantum Ising model.