Results for a critical threshold, the correction-to-scaling exponent and susceptibility amplitude ratio for 2d percolation

Details Results for a critical threshold, the correction-to-scaling exponent and susceptibility amplitude ratio for 2d percolation Results for a critical threshold, the correction-to-scaling exponent and susceptibility amplitude ratio for 2d percolation

2011-03-16

arxiv.org/abs/1103.3243v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

Talk presented at 24th Annual Workshop:"Recent Developments in Computer Simulational Studies in Condensed Matter Physics," Cen

Scientific paper

We summarize several decades of work in finding values for the percolation threshold p_c for site percolation on the square lattice, the universal correction-to-scaling exponent Omega, and the susceptibility amplitude ratio C^+/C^-, in two dimensions. Recent studies have yielded the precise values p_c = 0.59274602(4), Omega = 72/91 = 0.791, and C^+/C^- = 161.5(1.5), resolving long-standing controversies about the last two quantities and verifying the widely used value p_c = 0.592746 for the first.

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