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 perco lation threshold. The numerical simulations are-performed using an efficien t star-triangle algorithm. The percolation exponents, linked to the critica l behaviour at corners, are in good agreement with the conformal results. T he conductivity exponent, t' = zeta/nu, is found to be independent of the s hape of the system. Its value is very close to recent estimates for the sur face and bulk conductivity exponents.