Exact Solution of a Model of Localization
Exact Solution of a Model of Localization
The exact solution is presented for the "susceptibility," $\ensuremath{\chi}$ (the number of sites covered by the maximally extended eigenfunction), for the zero-energy solutions of a hopping model on a randomly dilute Cayley tree. If $p$ is the concentration, then $\ensuremath{\chi}\ensuremath{\sim}{({p}^{*}\ensuremath{-}p)}^{\ensuremath{-}1}$ with ${p}^{*}\ensuremath{\sim}{p}_{c}{e}^{\frac{1}{{\ensuremath{\xi}}_{1}}}$, where ${p}_{c}$ is the critical percolation concentration and …