A test of scaling near the bond percolation threshold

The bond percolation problem is studied by the Monte Carlo method on a two-dimensional square lattice of 2*10 6 bonds. Through the inclusion of a ghost field h, 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') are obtained as functions of two 'thermodynamic' variables, epsilon identical to (p c -p)/p c and h. The non-trivial problems associated with the identification of the singular parts of these functions are discussed and it is demonstrated that scaling holds for all three 'thermodynamic' functions within a rather large 'scaling region'.