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Axelrod's model with $F=2$ cultural features, where each feature can assume$k$ states drawn from a Poisson distribution of parameter $q$, exhibits acontinuous nonequilibrium phase transition in the square lattice. Here we useextensive Monte Carlo simulations and finite size scaling to study the criticalbehavior of the order parameter $\rho$, which is the fraction of sites thatbelong to the largest domain of an absorbing configuration averaged over manyruns. We find that it vanishes as $\rho \sim \left (q_c^0 - q \right)^\beta$with $\beta \approx 0.25$ at the critical point $q_c^0 \approx 3.10$ and thatthe exponent that measures the width of the critical region is $\nu^0 \approx2.1$. In addition, we find that introduction of long-range links by rewiringthe nearest-neighbors links of the square lattice with probability $p$ turnsthe transition discontinuous, with the critical point $q_c^p$ increasing from$3.1$ to $27.17$, approximately, as $p$ increases from $0$ to $1$. Thesharpness of the threshold, as measured by the exponent $\nu^p \approx 1$ for$p>0$, increases with the square root of the number of nodes of the resultingsmall-world network.

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