Site-bond percolation on simple cubic lattices: numerical simulation and analytical approach

Abstract

The site-percolation problem on simple cubic lattices has been studied by means of numerical simulation and analytical calculations based on exact counting of configurations on finite cells. Motivated by considerations of cluster connectivity, two distinct schemes (denoted as and ) have been considered. In (), two points are said to be connected if a sequence of occupied sites and (or) bonds joins them. Theoretical and numerical results, supplemented by analysis using finite-size scaling theory, were used to calculate the complete phase diagram of the system in the () space. Our study allowed us also to determine the critical exponents (and universality) characterizing the phase transition occurring in the system.