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Related Experiment Video

Updated: May 18, 2026

Trapping of Micro Particles in Nanoplasmonic Optical Lattice

Trapping of Micro Particles in Nanoplasmonic Optical Lattice

Published on: September 5, 2017

Explosive percolation on the Bethe lattice.

Huiseung Chae¹, Soon-Hyung Yook, Yup Kim

¹Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|September 26, 2012

Summary

This summary is machine-generated.

We developed a self-consistent simulation for percolation on the Bethe lattice. Achlioptas models exhibit continuous phase transitions, irrespective of specific growth rules, offering insights into network behavior.

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Area of Science:

Statistical Physics
Network Science
Computational Modeling

Background:

Percolation theory studies the formation of connected clusters in random networks.
The Bethe lattice, an infinite homogeneous Cayley tree, serves as a fundamental model for studying network properties.
Understanding phase transitions in complex systems is crucial for various scientific disciplines.

Purpose of the Study:

To develop a novel self-consistent simulation method for arbitrary percolation models on the Bethe lattice.
To characterize the phase transition behavior of different percolation models, including random bond and bootstrap percolation.
To investigate the impact of growth rules on the percolation transition in Achlioptas models.

Main Methods:

Development of a self-consistent simulation method based on order parameter (P∞) and mean cluster size (S) equations.
Application of the method to established percolation models (random bond, bootstrap) to derive prototype functions.
Comparative analysis of Achlioptas models (product and sum rules) against prototype functions.

Main Results:

Prototype functions for both continuous and discontinuous phase transitions were successfully obtained.
Self-consistent simulations revealed that Achlioptas models on the Bethe lattice exhibit continuous phase transitions.
The nature of the percolation transition in Achlioptas models was found to be independent of the specific growth rules employed.

Conclusions:

The developed self-consistent simulation method is effective for analyzing percolation on the Bethe lattice.
Achlioptas models demonstrate robust continuous phase transition behavior on the Bethe lattice.
This study provides a unified framework for understanding percolation transitions in complex network models.