We address the issue of universality in two-dimensional disordered Ising systems, by considering long, finite-width strips of ferromagnetic Ising spins with randomly distributed couplings. We calculate the free energy and spin-spin correlation functions (from which averaged correlation lengths, ξ ave , are computed) by transfer-matrix methods. An ansatz for the size-dependence of logarithmic corrections to ξ ave is proposed. Data for both random-bond and site-diluted systems show that pure system behaviour (with ν = 1) is recovered if these corrections are incorporated, discarding the weak-universality scenario.

Abstract. Finite-size corrections to scaling of critical correlation lengths and free energies of Ising and three-state Potts ferromagnets are analysed by numerical methods, on strips of width N sites of square, triangular and honeycomb lattices. Strong evidence is given that the amplitudes of the 'analytical' correction terms, N −2 , are identically zero for triangular and honeycomb Ising systems. For Potts spins, our results are broadly consistent with this lattice-dependent pattern of cancellations, though for correlation lengths non-vanishing (albeit rather small) amplitudes cannot be entirely ruled out.

Abstract. Numerical results for the first gap of the Lyapunov spectrum of the selfdual random-bond Ising model on strips are analysed. It is shown that finite-width corrections can be fitted very well by an inverse logarithmic form, predicted to hold when the Hamiltonian contains a marginal operator.

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The two-dimensional site percolation problem is studied by transfermatrix methods on finite-width strips with free boundary conditions. The relationship between correlation-length amplitudes and critical indices, predicted by conformal invariance, allows a very precise determination of the surface decay-of-correlations exponent, η s = 0.6664 ± 0.0008, consistent with the analytical value η s = 2/3. It is found that a special transition does not occur in the case, corroborating earlier series results. At the ordinary transition, numerical estimates are consistent with the exact value y s = −1 for the irrelevant exponent.