Journal of Physics A, Mathematical and General vol:24 issue:6 pages:1281-1291
A new ansatz is proposed to implement finite size scaling analysis of the dielectric breakdown model. Calculations on very small cells already allow to obtain good qualitative determinations of the fractal dimensions dBAR in a wide range of dimensionalities and model parameters. Exact enumerations or high accuracy Monte Carlo calculations on larger cells (less-than-or-equal-to 12 x 12) in d = 2 show a remarkable degree of convergence towards values known from large scale simulations for dBAR, and, to a lesser extent, for the multifractal dimension D(q) with q greater-than-or-equal-to -1. General difficulties inherent to Monte Carlo determinations of D(q) for negative q are also pointed out. For calculating the electrostatic potential inside these cells we use a new exact and fast algorithm, explained in detail in the appendix.