2000/09/30 by D. Karevski, Dragi Karevski, Yu‐Cheng Lin +7 · 3 citations
Mathematics · Physics and Astronomy · #Quantum many-body systems #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1007/pl00011100
10pages, 13figures, final form
arxiv created 2001/02/06 · openalex publication_date 2001/03/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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<αc, 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 αc=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 αc ≈ 4.5. Thus in the region 2<α<αc, where the central limit theorem holds for |ln J| the broadness of the distribution is relevant for the 2d quantum Ising model.