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Universality class of the two-dimensional randomly distributed growing-cluster percolation model
1Institut für Physik, Carl von Ossietzky Universität Oldenburg, D-26111 Oldenburg, Germany. oliver.melchert@uni-oldenburg.de
Summary
The cluster growth percolation (CGP) model on a square lattice shows a phase transition. Numerical simulations indicate this model belongs to the standard percolation universality class.
Area of Science:
- Statistical Physics
- Complex Systems
- Computational Physics
Background:
- The "Touch and Stop" cluster growth percolation (CGP) model simulates site occupation on a 2D lattice.
- Cluster growth is initiated from "seed" sites, with a fraction 'p' determining nucleation centers.
- Two growth styles, rhombic and disk-shaped, are considered.
Purpose of the Study:
- To investigate the critical behavior of the CGP model on a two-dimensional square lattice.
- To determine the critical exponents governing the percolation transition.
- To clarify the universality class of the CGP model.
Main Methods:
- Numerical simulations were performed on lattices up to size L=1024.
- Percolation probability and order parameter were analyzed.
- Finite-size scaling analysis was employed to determine critical exponents.
Main Results:
- For intermediate values of 'p', a spanning cluster of occupied sites emerges.
- Strong numerical evidence suggests the CGP model belongs to the standard percolation universality class.
- Critical exponents were determined with high precision.
Conclusions:
- The "Touch and Stop" CGP model exhibits a phase transition consistent with standard percolation theory.
- This finding contrasts with some previous studies and provides robust numerical validation.
- The model serves as a valuable testbed for understanding percolation phenomena.
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