UNIVERSALITY AND LOGARITHMIC CORRECTIONS IN 2-DIMENSIONAL RANDOM ISING-FERROMAGNETS

We address the question of weak versus strong universality scenarios f or the random-bond Ising model in two dimensions. A finite-size scalin g theory is proposed, which explicitly incorporates 1n L corrections ( L is the linear finite size of the system) to the temperature derivati ve of the correlation length. The predictions are tested by considerin g long, finite-width strips of Ising spins with randomly distributed f erromagnetic couplings, along which free energy, spin-spin correlation functions, and specific heats are calculated by transfer-matrix metho ds. 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 functi ons against distance yield average correlation lengths xi(av), whose s ize dependence agrees very well with the proposed theory. We also exam ine the size dependence of the specific heat, which clearly suggests a divergency in the thermodynamic limit. Thus our data consistently fav or the Dotsenko-Shalaev picture of logarithmic corrections (enhancemen ts) to pure system singularities, as opposed to the weak universality scenario.