On surface properties of two-dimensional percolation clusters

  title={On surface properties of two-dimensional percolation clusters},
  author={S.L.A. de Queiroz},
  journal={arXiv: Condensed Matter},
The two-dimensional site percolation problem is studied by transfer-matrix methods on finite-width strips with free boundary conditions. The relationship between correlation-length amplitudes and critical indices, predicted by conformal invariance, allows a very precise determination of the surface decay-of-correlations exponent, $\eta_s = 0.6664 \pm 0.0008$, consistent with the analytical value $\eta_s = 2/3$. It is found that a special transition does not occur in the case, corroborating… 
2 Citations

Tables from this paper

Percolation and conduction in restricted geometries
The finite-size scaling behaviour for percolation and conduction is studied in two-dimensional triangular-shaped random resistor networks at the percolation threshold. The numerical simulations are
Surface crossover exponent for branched polymers in two dimensions
Transfer-matrix methods on finite-width strips with free boundary conditions are applied to lattice site animals, which provide a model for randomly branched polymers in a good solvent. By assigning


Series expansion studies of percolation at a surface
Estimates of the local exponents gamma 1 and gamma 11 for the ordinary transition in the bond problem on the triangular lattice and bond and site problems on the face-centred cubic lattice, are
Correlation length in Ising strips with free and fixed boundary conditions
The correlation length of boundary spins in the Ising model, defined on strips of triangular lattice with free boundary conditions, is determined with an efficient numerical procedure based on the
Surface critical behaviour and local operators with boundary-induced critical profiles
The authors present a simple argument showing that the surface energy density of a semi-infinite d-dimensional spin system has, in general, a leading thermal singularity of the same form, mod T-Tc
Collapse of branched polymers
Exact calculations using transfer matrices on finite strips are performed to study the two-dimensional problem of one lattice animal with an attractive nearest neighbour interaction. Thermodynamic
Surface phase transitions in polymer systems
Self-avoiding walks, lattice trees, and related geometrical models provide a link between the physics of polymers and the study of critical phenomena. In particular, these models in the presence of a
Transfer-matrix approach to percolation and phenomenological renormalization
2014 A transfer-matrix method is used to calculate the correlation length for strips of finite width in the bond and site percolation problem. From the knowledge of these correlation lengths we
Universality of surface exponents of self-avoiding walks on a Manhattan lattice
The authors use phenomenological renormalization group techniques to study the bulk and surface properties of self-avoiding walks on a Manhattan lattice. They find that, as is the case for the bulk
The efficient determination of the percolation threshold by a frontier-generating walk in a gradient
The frontier in gradient percolation is generated directly by a type of self-avoiding random walk. The existence of the gradient permits one to generate an infinite walk on a computer of finite