Percolación discreta en redes tridimensionales

Abstract

Bond and site percolation on a three-dimensional lattice is studied. A bond (site) is occupied or empty with probability $p$ or $1-p$ respectively, for any size $N$. Through an exact numerical analysis, the different percolating trajectories are obtained as a function of its length $L$ for each three-dimensional cell. A polynomial function $f(p,N)$ associated to bond and site percolation. On each cell is determined, where symmetrical and asymmetrical cells are included in order to calculate the percolation thresholds and the critical exponent $\nu$, $\beta$ and $\gamma$ for each cell. Applying the finite size scaling techniques, these parameters are obtained in the thermodynamic limit. These results are in a good agreement with the similar ones obtained by means of other procedures and techniques described in literature for three-dimensional lattices.