Crossover from mean-field to 2d Directed Percolation in the contact process

We study the contact process on spatially embedded networks, consisting of a regular square lattice with long-range connections. To generate the networks, we start from a square lattice and, to each node i we add a long-range connection to a node j, selected at random from all possible nodes, with a weight rij−α per node. Extensive Monte Carlo simulations and a finite-size scaling analysis for different values of α reveal a crossover from the mean-field to 2d Directed Percolation universality class with increasing α, in the range 3<α<4.