Small-world behaviour in d-dimensional lattices

Small-world networks are lattice topologies with local features of regular networks and global features of random graphs, where a tunable parameter $p$ sets the degree of randomness of the system. Using large-scale simulations we find that the $\nu$ exponent of the correlation length of the lattice diverges at $p=0$ as $\xi=p^{-\nu}$ with $\nu= 1/d$ for dimensions $d$ up to three, confirming the renormalization group results of Newman and Watts.