Abstract
Results of an integral-equation approach to pair connectedness are given for lattice models, with emphasis on site percolation. The lowest-order approximation is expressible in terms of the lattice Green function and is isomorphic to a Polya random walk. It yields percolation exponents gamma =2, nu =1 for d=3 and gamma =1, nu =1/2 for d>or=4, d=dimension. For simple hypercubic lattices it also yields usefully sharp estimates for the site percolation threshold probability pP. A first correction is described.