Stochastic interpretation of the rate equation formulation of hopping transport theory. III. DC hopping analogues and their application to percolative conductance networks and spin systems

For Pt. II abstr. A70018 of 1974. DC hopping conductivity is independent of the weighting factors associated with the sites. It is shown that the weighting factors may be chosen so that the probability of N hops in time t is given by the Poisson distribution. This choice allows a simple derivation of the formula ¹/₂fd² for the DC diffusivity. Application of this formula to the hopping analogue of percolative conductance networks shows that their effective DC conductivity is proportional to the product of the fraction of bonds in the infinite cluster and d² for the infinite cluster. Application of the formula to the hopping analogue of percolative spin systems shows that the spin stiffness is proportional to the product of d² for the infinite cluster and the mean of the total exchange coupling constant associated with each site in the infinite cluster.