Random quantum magnets with broad disorder distribution

Details Random quantum magnets with broad disorder distribution Random quantum magnets with broad disorder distribution

2000-09-11

arxiv.org/abs/cond-mat/0009144v2

Physics

Condensed Matter

Statistical Mechanics

10pages, 13figures, final form

Scientific paper

10.1007/PL00011100

We study the critical behavior of Ising quantum magnets with broadly distributed random couplings (J), such that $P(\ln J) \sim |\ln J|^{-1-\alpha}$, $\alpha>1$, for large $|\ln J|$ (L\'evy flight statistics). For sufficiently broad distributions, $\alpha<\alpha_c$, the critical behavior is controlled by a line of fixed points, where the critical exponents vary with the L\'evy index, $\alpha$. In one dimension, with $\alpha_c=2$, we obtaind 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 $\alpha_c \approx 4.5$. Thus in the region $2<\alpha<\alpha_c$, where the central limit theorem holds for $|\ln J|$ the broadness of the distribution is relevant for the 2d quantum Ising model.

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