Specific heat singularity in two-dimensional random Ising ferromagnets

摘要

We use transfer-matrix methods to calculate free energies and specific heats on long, finite-width strips of Ising spins with randomly distributed ferromagnetic couplings. By implementation of our code on a highly parallel computer, we have managed to generate high-quality data for strip widths up to L = 18 sites. An unequivocal trend towards a divergency of the specific heat in the thermodynamic limit can be discerned. Finite-size data appear to behave halfway between a single-(In L) and double-(In In L) logarithmic dependence on strip width. This is in line with a crossover within the Dotsenko-Shalaev picture of logarithmic corrections to pure-system singularities.