Corrections to scaling and phenomenological renormalization for 2-dimensional percolation and lattice animal problems

Abstract

We continue and improve the transfer matrix approach of Derrida and de Seze by incorporating in two different ways the leading corrections to the asymptotic behaviour for wide strips. We find for the site percolation threshold in the square lattice pc = 0.59274 ± 0.00010, for the radius exponent of lattice animals 0.64075 ± 0.00015, and for the inverse growth factor or critical fugacity 0.246150 ± 0.000010 in the square lattice and 0.192925 ± 0.000010 in the triangular lattice. These results are consistent with, and sometimes more accurate than, the best estimates published before