A Test of Scaling for the Bond Percolation Threshold
Eugene Stanley
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Abstract
The bond percolation problem is studied by the Monte Carlo method on a two-dimensional square lattice of 2 X lo6 bonds. Through the inclusion of a ghost field h, we obtain the generating function (the percolation analogue of the Gibbs free energy), percolation probability (the analogue of the spontaneous magnetisation), and mean cluster size ('isothermal susceptibility') as functions of two 'thermodynamic' variables, c = ( p , -p ) / p c and h. We discuss the non-trivial problems associated with the identification of the singular parts of these functions. We demonstrate that scaling holds for all three 'thermodynamic' functions within a rather large 'scaling region'.
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De'pai'fs)le'Ill o/' P/vvsic's, Poslti%(ia Ur)i t't'i'sickest' Caloli('a, 22453 Ri o i'' Jair ei i o, BIa;i I
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