Critical properties in long-range hopping Hamiltonians

2004/07/07 by E. Cuevas
Physics and Astronomy · #cond-mat.dis-nn #cond-mat.mes-hall

paper · pdf · doi:10.1002/pssb.200404783

published as phys. stat. sol. (b) 241, 2109 (2004) · 9 pages, 6 .eps figures, contribution to the Festschrift for Michael Schreiber's 50th birthday

arxiv created 2004/07/07 · arxiv updated 2009/12/01

Abstract

Some properties of d-dimensional disordered models with long-range random hopping amplitudes are investigated numerically at criticality. We concentrate on the correlation dimension d₂ (for d=2) and the nearest level spacing distribution P_c(s) (for d=3) in both the weak (b^d ≫ 1) and the strong (b^d ≪ 1) coupling regime, where the parameter b^-d plays the role of the coupling constant of the model. It is found that (i) the extrapolated values of d₂ are of the form d₂=c_db^d in the strong coupling limit and d₂=d-a_d/b^d in the case of weak coupling, and (ii) P_ (s) has the asymptotic form P_c(s)∼exp (-A_ds^α) for s≫ , with the critical exponent α=2-a_d/b^d for b^d ≫ 1 and α=1+c_d b^d for b^d ≪ 1. In these cases the numerical coefficients A_d, a_d and c_d depend only on the dimensionality.

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