Correlation-length - exponent relation for the two-dimensional random Ising model

We consider the two-dimensional (2D) random Ising model on a diagonal strip of the square lattice, where the bonds rake two values, J(1)>J(2), with equal probability. Using an iterative method, based on a successive application of the star-triangle transformation, we have determined at the bulk critical temperature the correlation length along the strip xi(L) for different widths of the strip L less than or equal to 21. The ratio of the two lengths xi(L)/L = A is found to approach the universal value A = 2/pi for large L, independent of the dilution parameter J(1)/J(2). With our method we have demonstrated with high numerical precision, that the surface correlation function of the 2D dilute Ising model is self-averaging in the critical point conformally covariant and the corresponding decay exponent is eta(parallel to)=1.