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Lyapunov exponent (LE) of Anderson model with additional hopping
term to the second nearest neighbor, is analyzed within the second
order perturbation expansion in strength of diagonal disorder.
Depending on hopping integrals, there are two propagating channels
in a range of energies. By comparison with exact numerical results,
we show that naive perturbation theory fails to give accurate
Lyapunov exponents at such energies. New anomalies of Kappus-Wegner
type emerge when hopping to second neighbor is allowed which are
non-universal in the sense that is described below. It is shown that
suitable averages in the first order of perturbation theory, develop
singularities at these anomalous energies which enable us to locate
them.
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