Print Email Facebook Twitter Percolation transitions in two dimensions Title Percolation transitions in two dimensions Author Feng, X. Deng, Y. Blöte, H.W.J. Faculty Applied Sciences Department Radiation, Radionuclides and Reactors Date 2008-09-30 Abstract We investigate bond- and site-percolation models on several two-dimensional lattices numerically, by means of transfer-matrix calculations and Monte Carlo simulations. The lattices include the square, triangular, honeycomb kagome, and diced lattices with nearest-neighbor bonds, and the square lattice with nearest- and next-nearest-neighbor bonds. Results are presented for the bond-percolation thresholds of the kagome and diced lattices, and the site-percolation thresholds of the square, honeycomb, and diced lattices. We also include the bond- and site-percolation thresholds for the square lattice with nearest- and next-nearest-neighbor bonds. We find that corrections to scaling behave according to the second temperature dimension Xt2=4 predicted by the Coulomb gas theory and the theory of conformal invariance. In several cases there is evidence for an additional term with the same exponent, but modified by a logarithmic factor. Only for the site-percolation problem on the triangular lattice does such a logarithmic term appear to be small or absent. The amplitude of the power-law correction associated with Xt2=4 is found to be dependent on the orientation of the lattice with respect to the cylindrical geometry of the finite systems. Subject bonds (chemical)lattice theoryMonte Carlo methodspercolation To reference this document use: http://resolver.tudelft.nl/uuid:68f9f8de-e483-4bce-b1a9-828eb52ee99b Publisher American Physical Society ISSN 1539-3755 Source Physical Review E, 78 (3 pt 1), 2008 Part of collection Institutional Repository Document type journal article Rights (c) 2008 Feng, X. ; Deng, Y. ; Blöte, H.W.J. ; American Physical Society Files PDF Feng_2008.pdf 90.98 KB Close viewer /islandora/object/uuid:68f9f8de-e483-4bce-b1a9-828eb52ee99b/datastream/OBJ/view