Eur. Phys. J. B 20, 267-276 (2001)
https://doi.org/10.1007/PL00011100

Random quantum magnets with broad disorder distribution

¹ Laboratoire de Physique des Matériaux (UMR 7556 CNRS) , Université Henri Poincaré (Nancy 1), BP 239, 54506 Vandœuvre lès Nancy Cedex, France
² NIC, Forschungszentrum Jülich, 52425 Jülich, Germany
³ Theoretische Physik, Universität des Saarlandes, 66041 Saarbrücken, Germany
⁴ Department of Physics, Tokyo Metropolitan University, 192-0397 Tokyo, Japan
⁵ Research Institute for Solid State Physics and Optics, PO Box 49, 1525 Budapest, Hungary
⁶ Institute for Theoretical Physics, Szeged University, 6720 Szeged, Hungary

Corresponding author: ^a igloi@power.szfki.kfki.hu

Received: 6 December 2000
Revised: 22 January 2001
Published online: 15 March 2001

Abstract

We study the critical behavior of Ising quantum magnets with broadly distributed random couplings (J), such that , , for large (Lévy flight statistics). For sufficiently broad distributions, , the critical behavior is controlled by a line of fixed points, where the critical exponents vary with the Lévy index, α. In one dimension, with , 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 . Thus in the region , where the central limit theorem holds for the broadness of the distribution is relevant for the 2d quantum Ising model.