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Leaf-excluded percolation in two and three dimensions.

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This summary is machine-generated.

We developed a new leaf-excluded percolation model. This model precisely estimates critical thresholds on square and cubic lattices, showing its phase transition belongs to the standard percolation universality class.

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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.