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
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.
PACS: 75.50.Lk – Spin glasses and other random magnets / 05.30.Ch – Quantum ensemble theory / 75.10.Nr – Spin-glass and other random models / 75.40.Gb – Dynamic properties (dynamic susceptibility, spin waves, spin diffusion, dynamic scaling, etc.)
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2001