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The Universal Amplitude Ratio $Γ^{-}/Γ^{+}$ for Two-Dimensional Percolation

Iwan Jensen·Robert M. Ziff
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Abstract

The amplitude ratio of the susceptibility (or second size-moment) for two-dimensional percolation is calculated by two series methods and also by Monte-Carlo simulation. The first series method is a new approach based upon integrating approximations to the scaling function. The second series method directly uses low- and high-density series expansions of the susceptibility, going to unprecedented orders for both bond and site percolation on the square lattice. Putting all methods together we find a consistent value $Γ^{-}/Γ^{+} = 162.5 \pm 2$, a significant improvement over previous results that placed the value of this ratio variously in the range of 14 to 220.

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Iwan Jensen, Robert M. Ziff. 2006-07-06. The Universal Amplitude Ratio $Γ^{-}/Γ^{+}$ for Two-Dimensional Percolation. https://doi.org/10.1103/physreve.74.020101

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