A Dynamical Flux Expansion for the Three-Dimensional Bond Percolation Problem
A new expansion for treating diffusive transport on bond disordered lattices is presented and applied to the bond percolation problem in 3 dimensions. Our approach, when combined with standard resummation techniques, leads to a prediction for the 3-dimensional transport threshold pc = 0.252, which is in excellent agreement with known results. This agreement is obtained without recourse to renormalization group techniques or self-consistent arguments. It originates from a new t-matrix representation for the frequency-dependent diffusion coefficient and is a direct consequence of the equations of motion for the probability currents.
P. E. Parris et al., "A Dynamical Flux Expansion for the Three-Dimensional Bond Percolation Problem," Physica A: Statistical Mechanics and its Applications, vol. 151, no. 1, pp. 144-152, Elsevier, Jul 1988.
The definitive version is available at https://doi.org/10.1016/0378-4371(88)90044-1
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