Percolação explosiva em redes quadradas

Abstract

In this study, we analyze the Percolation Theory and its properties, showing how it appears in the construction of random networks. We developed the mathematical basis used in Network Theory and its application at the critical point of the system, in order to understand the physical nature of the transition. Our focus is the phenomenon of percolation in square lattice, as well as the consequences for this phenomenon when we implement a choice in the process of adding bonds, for that we include the Achlioptas process in the Ziff-Newmam algorithm. We present some works focusing on explosive percolation, on random and square networks, and the necessary conditions for the transition to be abrupt. The results compare three different models that vary in relation to the value of a parameter α, which can favor redundant or merging bonds, generating a global correlation between the clusters and modifying their robustness.