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

TL;DR

This study investigates the phase transition in a 2D cluster growth percolation model, finding it belongs to the standard percolation universality class through extensive numerical simulations and finite-size scaling analysis.

Contribution

The paper provides the first detailed finite-size scaling analysis of the

Findings

The CGP model exhibits a continuous phase transition.

Critical exponents match those of standard percolation.

Numerical evidence supports the universality class conclusion.

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.