Phase diagram of site-bond percolation

M. I. GONZALEZ; P. CENTRES; A. J. RAMIREZ PASTOR; WALTER LEBRECHT

Valdivia

Conferencia; XIX Conference on Nonequilibrium Statistical Mechanics and Nonlinear Physics; 2016

The site-percolation problem on square, triangular and simple cubic lattices has been studiedby means of numerical simulation and analytical calculations based on exact counting ofconfigurations on finite cells [1-5]. Motivated by considerations of cluster connectivity, twodistinct schemes (denoted as STB and SSB) have been analyzed. In STB(SSB),two points are said to be connected if a sequence of occupied sites AND (OR) bonds joinsthem.In order to obtain the percolation functions corresponding to STB and SSB sitebondpercolation, operations AND (Series) and OR (Parallel) proposed by Tsallis [6] wereconsidered. The percolation threshold was obtained by numerical simulation using theHoshen-Kopelman algorithm. Then, the percolation thresholds were obtained by analyticalcalculations based on exact counting on all possible configurations that are presents on afinite cell. A good qualitative agreement between numerical and theoretical data was found,especially in the case of square lattices. However, appreciable differences were observed forS∩B criterion in the case of triangular and simple cubic lattices.