A second spanning cluster is drawn at on an lattice from a different seed and…
PHYSICS · Multi-part · Fermi University Physics · Computational Physics · Thermal, Statistical & Complex Systems · Monte Carlo and lattice simulation of physical systems
Computational Physics, Ch Rules on a lattice: diffusion, percolation and growth
Problem
A second spanning cluster is drawn at p=0.593 on an L=2048 lattice from a different seed and box-counted about the occupied site nearest its own centroid, exactly as in the text. The counts Ncl(R) inside a box of half-width R areRNcl(R)2124318110165433220136482861282794620067228
((a)) Fit a straight line to logNcl against logR over all eight points and report the slope with the standard error the fit returns.
((b)) The exact value for a percolation cluster at the threshold in two dimensions is 91/48. Say how far the measurement sits from it, in units of its own uncertainty, and whether the two agree.
((c)) Refit using only the four points with R≤16. Report that slope, say how much range it covers, and say whether the number may be called a fractal dimension.