Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2006-04-26
Physics
Condensed Matter
Disordered Systems and Neural Networks
5 pages, no figures. Version accepted for publication on International Journal of Modern Physics B
Scientific paper
We prove that a strongly disordered two-dimensional system localizes with a localization length given analytically. We get a scaling law with a critical exponent is $\nu=1$ in agreement with the Chayes criterion $\nu\ge 1$. The case we are considering is for off-diagonal disorder. The method we use is a perturbation approach holding in the limit of an infinitely large perturbation as recently devised and the Anderson model is considered with a Gaussian distribution of disorder. The localization length diverges when energy goes to zero with a scaling law in agreement to numerical and theoretical expectations.
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