ISSN:
1434-6036
Keywords:
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.)
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract: We study the critical behavior of Ising quantum magnets with broadly distributed random couplings (J), such that P(ln J) ∼ | ln J|-1 - α, α 〉 1, for large | ln J| (Lévy flight statistics). For sufficiently broad distributions, α 〈 , 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 = 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 ≈ 4.5. Thus in the region 2 〈 α 〈 , where the central limit theorem holds for | ln J| the broadness of the distribution is relevant for the 2d quantum Ising model.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/PL00011100
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