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Related Experiment Video

Updated: May 10, 2026

Fabrication and Visualization of Capillary Bridges in Slit Pore Geometry

Fabrication and Visualization of Capillary Bridges in Slit Pore Geometry

Published on: January 9, 2014

Bond and site percolation in three dimensions.

Junfeng Wang¹, Zongzheng Zhou, Wei Zhang

¹Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.

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

|June 18, 2013

Summary

This study precisely estimates critical exponents for bond and site percolation models on a cubic lattice. Findings reveal new insights into finite-size corrections and universal amplitudes in critical phenomena.

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Area of Science:

Statistical Physics
Computational Physics
Materials Science

Background:

Percolation theory is crucial for understanding connectivity in disordered systems.
Accurate estimation of critical exponents and amplitudes is essential for universality class identification.

Purpose of the Study:

To precisely determine percolation thresholds and critical exponents for bond and site percolation on a simple-cubic lattice.
To investigate universal amplitudes and finite-size correction effects.

Main Methods:

Extensive Monte Carlo simulations on simple-cubic lattices up to L=512.
Analysis of critical points, critical exponents, and various universal amplitudes.

Main Results:

Estimated bond percolation threshold p(c)(bond)=0.24881182(10) and site percolation threshold p(c)(site)=0.3116077(2).
Calculated critical exponents including 1/ν=1.1410(15) and β/ν=0.47705(15).
Observed leading finite-size corrections in wrapping probabilities governed by an exponent ≈-2, deviating from the predicted y(i)≈-1.2.

Conclusions:

The study provides highly accurate critical exponents and amplitudes for cubic lattice percolation.
Discrepancies in finite-size correction exponents suggest potential nuances in universality or model behavior.