• DOI:10.1103/PHYSREVE.78.031136
• Corpus ID: 29282598

Percolation transitions in two dimensions.

@article{Feng2008PercolationTI,
  title={Percolation transitions in two dimensions.},
  author={Xiaomei Feng and Youjin Deng and Henk W. J. Bl{\"o}te},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2008},
  volume={78 3 Pt 1},
  pages={
          031136
        }
}

• Xiaomei Feng, Youjin Deng, H. Blöte
• Published 30 September 2008
• Physics
• Physical review. E, Statistical, nonlinear, and soft matter physics

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 X_{t2}=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 X_{t2}=4 is found to be dependent on the orientation of the lattice with respect to the cylindrical geometry of the finite systems.