Abstract

An empirical polynomial equation ps(pb)=A+Kpbn is proposed to describe the behavior of critical frontiers for mixed site-bond percolation systems. This equation successfully recovers the logarithmic equation proposed by Yanuka & Englman, as well as the hyperbolic equation proposed by Tarasevich & van der Marck. For the latter, an analytical development is proposed using the logical operations provided by Tsallis on the S∩B and S∪B phases. The empirical equation proposed for n=4 successfully describes the critical S∪B frontier for square, hexagonal, triangular and Kagome lattices. An extension of this equation is performed for simple systems linked as dimers in square and triangular lattices. © 2025 Elsevier B.V.