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

TL;DR

This paper uses large-scale Monte Carlo simulations to verify the critical scaling behavior of models with combined short- and long-range interactions, including the Hastings long-range model and small-world network models.

Contribution

It provides the first large-scale simulation verification of Hastings' predicted critical scaling in models with mixed interactions.

Findings

Confirmed Hastings' critical scaling predictions for all models

Validated the use of Monte Carlo simulations for complex network models

Demonstrated the universality of critical behavior in small-world and long-range models

Abstract

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.