Random adsorption process of linear k-mers on square lattices under the Achlioptas process

We study the explosive percolation with k-mer random sequential adsorption (RSA) process. We consider both the Achlioptas process (AP) and the inverse Achlioptas process (IAP), in which giant cluster formation is prohibited and accelerated, respectively. By employing finite-size scaling analysis, we confirm that the percolation transitions are continuous, and thus we calculate the percolation threshold and critical exponents. This allows us to determine the universality class of the k-mer explosive percolation transition. Interestingly, the numerical simulation suggests that the universality class of the explosive percolation transition with the AP alters when the k-mer size changes. In contrast, the universality class of the transition with the IAP is independent of k, but it differs from that of the RSA without the IAP.

Automated summary

In this study, we investigate explosive percolation with k-mer random sequential adsorption process. We analyze both the Achlioptas process (AP) and the inverse Achlioptas process (IAP) and determine the percolation threshold and critical exponents using finite-size scaling analysis. The results show that the percolation transitions are continuous, and the universality class of the k-mer explosive percolation transition can be determined.