The universality class of the continuous phase transition in the 2D "Touch and Stop" cluster growth percolation model

Abstract: 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 spans 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 (2010) 041108], we find strong numerical evidence that the CGP model is in the standard percolation universality class.