Percolation and conduction in restricted geometries

The finite-size scaling behaviour for percolation and conduction is studied in two-dimensional triangular-shaped random resistor networks at the percolation threshold. The numerical simulations are performed using an efficient star-triangle algorithm. The percolation exponents, linked to the critical behaviour at corners, are in good agreement with the conformal results. The conductivity exponent, t ´ = / , is found to be independent of the shape of the system. Its value is very close to recent estimates for the surface and bulk conductivity exponents.