Universality class of the two-dimensional randomly distributed growing-cluster percolation model.

We consider the "Touch and Stop" cluster growth percolation (CGP) model on the two-dimensional square lattice. A key parameter in the model is the fraction p of occupied "seed" sites that act as nucleation centers from which a particular cluster growth procedure is started. Here, we consider two growth styles: rhombic and disk-shaped cluster growth. For intermediate values of p the final state, attained by the growth procedure, exhibits a cluster of occupied sites that span the entire lattice. Using numerical simulations we investigate the percolation probability and the order parameter and perform a finite-size scaling analysis for lattices of side length up to L=1024 in order to carefully determine the critical exponents that govern the respective transition. In contrast to previous studies, reported in Tsakiris et al. [Phys. Rev. E 82, 041108 (2010)], we find strong numerical evidence that the CGP model is in the standard percolation universality class.