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.
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