Percolation in networks with long-range connections

Two-dimensional lattices of points are connected with long-range links, whose lengths are distributed according to P(r)similar to r(-alpha). By changing the decay exponent a one can go from d-dimensional short-range networks to infinity-dimensional networks topologically similar to random graphs. Percolation on these networks is numerically studied for systems of up to 10(7) sites. The shortest-path, fractal and chemical dimensions are determined at the critical threshold, as a function of the decay exponent a. (c) 2006 Elsevier B.V. All rights reserved.