Monte Carlo Simulation of Small-World Models with Weak Long-Range Interactions

Large-scale Monte Carlo simulations, together with scaling, are used to obtain the critical behavior of the Hastings long-range model and two corresponding models based on small-world networks. These models have combined short- and long-range interactions. For all three models, the critical scaling behavior predicted by Hastings [Phys. Rev. Lett. 91, 098701] is verified.