PERCOLATION ON THE SQUARE LATTICE IN A LXM GEOMETRY - ANALYSIS OF PERCOLATION CLUSTERS PROPERTIES

A study of the site percolation model on the square lattice in a L x M geometry at critically is presented. For L much less than M one observes the growth of numerous percolation clusters in the L-direction in contrast to the absence of percolation in the M-direction. Consequently, relevant properties of these clusters such us for example the average number of clusters (N(CL)), the cluster length distribution (P(l, L), with l=cluster length in the M direction) and average cluster length (l(CL)), are studied by means of the Monte Carlo technique and analyzed on the basis of finite-size scaling arguments. The following behavior is found: N(CL)is-approximately-equal-to (3/8) (L/M)-delta, with delta = 1; and l(CL) is-approximately-equal-to 2.0 L. Also the distribution P(1, L) is of the exponential-exponential type and their characteristic exponents are evaluated.