Leaf-excluded percolation in two and three dimensions

Area of Science:

• Statistical Physics
• Network Science
• Computational Physics

Background:

• Percolation theory studies the formation of connected clusters in random networks.
• Leaves (vertices of degree one) can influence percolation properties.
• Understanding phase transitions in modified percolation models is crucial for various scientific fields.

Purpose of the Study:

• Introduce and analyze the leaf-excluded percolation model.
• Precisely estimate critical thresholds for this model on square and simple-cubic lattices.
• Determine the universality class of the leaf-excluded model's phase transition.

Main Methods:

• Monte Carlo simulations were employed to study the leaf-excluded model.
• A worm-like algorithm was utilized for efficient simulation.
• Wrapping probabilities were analyzed to estimate critical thresholds.

Main Results:

• Critical thresholds were precisely estimated for the square lattice (0.3552475(8)) and simple-cubic lattice (0.185022(3)).
• Estimates for thermal and magnetic exponents align with standard percolation values.
• The leaf-excluded model's phase transition was found to belong to the standard percolation universality class.

Conclusions:

• The leaf-excluded percolation model provides a refined understanding of network connectivity.
• The model's phase transition behavior is consistent with established percolation universality classes.
• This research contributes to the fundamental understanding of phase transitions in disordered systems.