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We show analytically that the apparent non-analyticity discovered recently inthe inverse participation ratio (IPR) of the eigenstates in Anderson's model oflocalization is also present in a simple two-site model, along with aconcurrent non-analyticity in the density of states (DOS) at the same energy.We demonstrate its evolution from two sites to the thermodynamic limit bynumerical methods. For the two site model, non-analyticity in higherderivatives of the DOS and IPR is also proven to exist for all boundeddistributions of disorder.

Singular Behavior of Anderson Localized Wavefunctions for a Two-Site Model