  We address the question of weak versus strong universality scenarios for the
random-bond Ising model in two dimensions. A finite-size scaling theory is
proposed, which explicitly incorporates $\ln L$ corrections ($L$ is the linear
finite size of the system) to the temperature derivative of the correlation
length. The predictions are tested by considering long, finite-width strips of
Ising spins with randomly distributed ferromagnetic couplings, along which free
energy, spin-spin correlation functions and specific heats are calculated by
transfer-matrix methods. The ratio $\gamma/\nu$ is calculated and has the same
value as in the pure case; consequently conformal invariance predictions remain
valid for this type of disorder. Semilogarithmic plots of correlation functions
against distance yield average correlation lengths $\xi^{av}$, whose size
dependence agrees very well with the proposed theory. We also examine the size
dependence of the specific heat, which clearly suggestsa divergency in the
thermodynamic limit. Thus our data consistently favour the Dotsenko-Shalaev
picture of logarithmic corrections (enhancements) to pure system singularities,
as opposed to the weak universality scenario.
