Effect of long-range interactions on the phase transition of Axelrod's model

Axelrod's model with F=2 cultural features, where each feature can assume k states drawn from a Poisson distribution of parameter q, exhibits a continuous nonequilibrium phase transition in the square lattice. Here we use extensive Monte Carlo simulations and finite-size scaling to study the critical behavior of the order parameter ρ, which is the fraction of sites that belong to the largest domain of an absorbing configuration averaged over many runs. We find that it vanishes as ρ∼(q_{c}^{0}-q)^{β} with β≈0.25 at the critical point q_{c}^{0}≈3.10 and that the exponent that measures the width of the critical region is ν^{0}≈2.1. In addition, we find that introduction of long-range links by rewiring the nearest-neighbors links of the square lattice with probability p turns the transition discontinuous, with the critical point q_{c}^{p} increasing from 3.1 to 27.17, approximately, as p increases from 0 to 1. The sharpness of the threshold, as measured by the exponent ν^{p}≈1 for p>0, increases with the square root of the number of nodes of the resulting small-world network.