MULTISCALING BEHAVIOR IN THE CROSSOVER BETWEEN SURFACE AND BULK CRITICAL EXPONENTS FOR PERCOLATION IN 2 DIMENSIONS

The crossover between the surface and bulk values of the order-parameter critical exponent (P) is investigated for the site-percolation model in a rectangular geometry (L X M, L <<M) with free boundary conditions. Due to the reduction in the connectivity, when the space is cut by the surfaces of the sample which cannot be penetrated by the percolating clusters, beta decays exponentially from the surface value beta(s) congruent to 0.40) to the bulk value (beta(b)=5/36). This decay is interpreted in terms of multiscaling which implies that each row of the percolating cluster (taken in the M direction) has its own, scaling and consequently a different fractal dimension.