Simulações numéricas de percolação em redes bidimensionais

Abstract

Percolation theory is a fundamental model in statistical physics used to study connectivity in disordered systems. In this work, numerical simulations of percolation on two-dimensional lattices are performed using the Hoshen-Kopelman algorithm combined with the Monte Carlo method. Site and bond percolation models on square lattices are analyzed with the goal of estimating the critical percolation threshold pc, characterizing the growth of the largest cluster, and investigating the cluster size distribution. The results accurately reproduce well-known critical behaviors from the literature, such as the second-order phase transition and power law distribution at the critical point. This study confirms the robustness of the implemented algorithms and provides a solid foundation for future applications in complex systems and real-world networks.