Searching for a New Type of Surface Percolation on a 3D lattice

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We consider a new surface percolation problem on a 3D simple cubic lattice through numerical simulation. In this problem, randomly occupied surfaces initially form an infinite cluster at p = 0.21, where p is the surface occupation probability. This site percolation problem is well-studied. The infinite cluster at this value of p, however, contains many “hole”, since surfaces are considered to be connected if they share at least one edge in common. As p increases over that value, these holes are gradually filled with surfaces. We find that, at p = 0.66, there is a sharp transition where the infinite cluster contains one sheet with complicated folds. We also numerically evaluate the critical exponents Beta and nu using finite size scaling method and obtain Beta = 0.3 and nu = 1.0. We cannot find this combination of the values in any sets of critical exponents well-known at present. This fact may suggest that our surface percolation problem belongs to a new universality class.

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Journal: TechConnect Briefs
Volume: 2, Technical Proceedings of the 2002 International Conference on Computational Nanoscience and Nanotechnology
Published: April 22, 2002
Pages: 419 - 422
Industry sector: Advanced Materials & Manufacturing
Topics: Informatics, Modeling & Simulation
ISBN: 0-9708275-6-3