Harris, A. Brooks2023-05-232023-05-231982-07-262015-08-11https://repository.upenn.edu/handle/20.500.14332/43020The 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*~pce1/ξ1, 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.PhysicsQuantum PhysicsArticle