Universality of the spectral dimension of percolation clusters

We have calculated, via an extensive Monte Carlo simulation, the spectral dimension ̃ \~d of infinite percolation clusters, at different Euclidean dimensions $2<~d<~6$ and d=∞. ̃ \~d is extracted from the asymptotic behavior of the average number SN of distinct visited sites during an N-step random walk. Correction to scaling is shown to be very important. For all $d>~2$, SN takes the following form: SN=aNˢ(1+bN^-ωa), where s= ̃ \~d2, $0.661<~s<~0.666$, and ω1/6. We compare our results with existing theories or conjectures relative to the value of ̃ \~d.