The exact solution is presented for the "susceptibility," χ (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 χ~(p*-p)^-1 with p*~pce^1ξ₁, where pc is the critical percolation concentration and ξ₁ the one-dimensional localization length. This result is argued to hold for the dilute quantum Heisenberg antiferromagnet at zero temperature.
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A. B. Harris (1982) studied this question.
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