Phenomenological renormalisation of Monte Carlo data for percolation

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Abstract
The accuracy of a phenomenological renormalisation which is based on Monte Carlo data is tested by investigating site percolation in a simple cubic lattice. The method appears to be very accurate and can yield precise estimates of the quantities of interest with small to moderate lattice sizes. The site percolation threshold of the lattice is predicted to be 0.3115+or-0.0005. If nu is the exponent of correlation length, the author finds beta / nu approximately=0.48+or-0.01 for the exponent of percolation probability and beta B/ nu approximately=1.1+or-0.03 for the backbone exponent, in agreement with most accurate data currently available. An analysis of the data at the percolation threshold based on the standard finite-size scaling method also supports the results.