Boundary effects for invasion percolation are introduced and discussed here. The presence of boundaries determines a set of critical exponents characteristic of the boundary. In this paper we present numerical simulations showing a remarkably different fractal dimension for the region of the percolating cluster near the boundary. In fact, near the surface we find a value of $D^{\mathrm{sur}}=1.67\mathrm{}\pm 0.03,$ with respect to the bulk value of $D^{\mathrm{bul}}=1.87\mathrm{}\pm \mathrm{0.01.}$ Furthermore, we are able to present a theoretical computation of the fractal dimension near the boundary in fairly good agreement with numerical data.

• Received 13 May 1997

DOI:https://doi.org/10.1103/PhysRevE.56.R1291