Mixed percolation as a bridge between site and bond percolation

Abstract

By using mixed percolation as a bridge between site and bond percolation, we derive a new inequality between the critical points of these processes that is optimal in a certain sense. We also extend a result on the crossover exponent of bond-diluted Potts models to site-diluted Potts models. Some newresults about the critical line in mixed percolation are also proved. 1. Introduction. Bond and site percolation are similar processes in various respects, and it is easy to overlook their differences and miss the fact that their comparison may sometimes be interesting and challenging. The issues addressed in this paper include a nontrivial relationship between the critical points of these two processes and a nontrivial extension to the site percolation setting of a result on diluted Potts models that was only available in the bond percolation setting. For these purposes, we study mixed site–bond percolation, which can be seen as a smooth bridge between site and bond percolation. As a by-product of our approach, we also derive some new results on the critical line in mixed percolation.