The nature of percolation 'channels'

A relation is found between the percolation probability, P(s)(x), for site percolation, the conductance, G(x), of certain random networks, and the spin-stiffness coefficient, D(x), of dilute Heisenberg ferromagnet. Numerical results and critical exponents for these quantities near their common threshold are reported. These results demonstrate that the percolation 'channels' in which spin waves occur cannot be regarded as one or two dimensional. © 1973.