




The cluster density is n_{c,L}(p) = N^{1} ∑_{k} a_{k} p^{k} (1p)^{Nk} with N=L^{2} (for site percolation) or N=2 L^{2} (for bond percolation) and the a_{k} taken from the data files.
Exact cluster densities for site percolation on 2d lattices with periodic boundary conditions:
triangular  3×3  4×4  5×5  6×6  7×7 

square  3×3  4×4  5×5  6×6  7×7 
nnsquare^{(a)}  3×3  4×4  5×5  6×6  7×7 
unionjack  4×4  6×6  
hexagonal  4×4  6×6 
Exact cluster densities for site percolation on 2d lattices with open boundary conditions:
triangular  3×3  4×4  5×5  6×6  7×7  8×8  9×9  10×10  11×11  12×12  13×13  14×14  15×15  16×16 

square  3×3  4×4  5×5  6×6  7×7  8×8  9×9  10×10  11×11  12×12  13×13  14×14  15×15  16×16 
nnsquare^{(a)}  3×3  4×4  5×5  6×6  7×7  8×8  9×9  10×10  11×11  12×12  13×13  14×14  15×15  16×16 
R^{b} is the probability that it wraps in both dimensions.
triangular  3×3  4×4  5×5  6×6  7×7 

square  3×3  4×4  5×5  6×6  7×7 
nnsquare^{(a)}  3×3  4×4  5×5  6×6  7×7 
unionjack  4×4  6×6  
hexagonal  4×4  6×6 
R^{e} is the probability that a configuration wraps in either dimension.
triangular  3×3  4×4  5×5  6×6  7×7 

square  3×3  4×4  5×5  6×6  7×7 
nnsquare^{(a)}  3×3  4×4  5×5  6×6  7×7 
unionjack  4×4  6×6  
hexagonal  4×4  6×6 
R^{v} is the probability of wrapping around the vertical dimension:
square  3×3  4×4  5×5  6×6  7×7  8×8  9×9  10×10  11×11 

nnsquare^{(a)}  3×3  4×4  5×5  6×6  7×7  8×8  9×9  10×10  11×11 
triangular  3×3  4×4  5×5  6×6  7×7  8×8  9×9  10×10  11×11 

square  3×3  4×4  5×5  6×6  7×7  8×8  9×9  10×10  11×11 
nnsquare^{(a)}  3×3  4×4  5×5  6×6  7×7  8×8  9×9  10×10  11×11 
^{(a)} The nnsquare lattice is the square lattice with additional next nearest neighbor links (Moore neighborhood).





© by Stephan Mertens (Datenschutzerklärung)
updated on Tuesday, August 23rd 2022, 10:06:30 CET;