DYNAMIC STRUCTURE FACTOR OF PERCOLATION CLUSTERS AT CRITICALITY

The dynamic structure factor of very large percolating clusters (bond and site), in two dimensions and three dimensions are calculated using the spectral moments method. Interactions are represented by the scal ar model. Numerical results are presented and interpreted in terms of scaling arguments given by Alexander, Courtens and Vacher (ACV) in 199 3. Concerning the q lambda << 1 limit, our results confirm and supplem ent previous numerical work and are in agreement with the scaling beha viour theoretically deduced by ACV. Concerning the q lambda >> 1 limit , we have shown that the dynamic structure factor complies with the ve ry nice asymptotic behaviour g(q, omega) = q(y)H(q lambda(omega)) wher e the scaling function H(x) is of power-law form x(-tau') in agreement with the theory. However, our results indicate a scaling behaviour wi th exponents that differ from those deduced by theory. The values obta ined for tau' are 1.20 for the two-dimensional bond and site percolati ng lattices, and 1.00 for the three-dimensional percolating lattices. Comparisons with previous simulations are reported.