Probability of Incipient Spanning Clusters in Critical Two-Dimensional Percolation

The probability of simultaneous occurence of at least k spanning clusters has been studied by Monte Carlo simulations on the 2D square lattice at the bond percolation threshold Pc=1/2. The calculated probabilities for free boundary conditions and periodic boundary conditions are in a very good coincidence with the exact formulae developed recently by Cardy.Comment: Contribution to Lattice 97, LaTeX, 3 pages, 4 figures (1-eps, 3- LaTeX

On the quality of random number generators with taps

Recent exact analytical results developed for the random number generators with taps are reported. These results are applicable to a wide class of algorithms, including random walks, cluster algorithms, Ising models. Practical considerations on the improvement of the quality of random numbers are discussed as well.Comment: Conference on Computational Physics, Granada, Spain, 199