Percolação em redes isotropicamente direcionadas

Abstract

We investigate percolation on a randomly directed lattice, an intermediate between standard percolation and directed percolation models, focusing on the isotropic case in which bonds on opposite directions occur with the same probability. We derive exact results for the percolation threshold on honeycomb and triangular lattices, and present a conjecture for the value the percolation-threshold for in any lattice os given for $p_2 + p_1/2 = p_c$, where $p_c$ é standard critical percolation, $p_1$ is the probability of the lattice have a directed link and $p_2$ is the probability of the lattice have a undirected link that we call mixed-link lattices. We also identify presumably universal critical exponents, including a fractal dimension, associated with the strongly-connected components both for planar and cubic lattices. These critical exponents are different from those associated either with standard percolation or with directed percolation. In another perspective, begin mixed-link square lattices, we study the optimal paths and optimal crack paths in the lattices with directed links and undirected links and we found that optimal path critical exponents are the same for both standard percolation and isotropically directed lattices. However, the critical exponents from optimal path cracks are completely diferent in both lattice types and energy landscape disordered.