Domain-wall energies and magnetization of the two-dimensional random-bond Ising model

We study ground-state properties of the two-dimensional random-bond Ising model with couplings having a concentration $p∊[0,1]$ of antiferromagnetic and (1-p) of ferromagnetic bonds. We apply an exact matching algorithm which enables us the study of systems with linear dimension L up to $700$. We study the behavior of the domain-wall energies and of the magnetization. We find that the paramagnet-ferromagnet transition occurs at pc~0.103 compared to the concentration pₙ~0.109 at the Nishimori point, which means that the phase diagram of the model exhibits a re-entrance. Furthermore, we find no indications for an (intermediate) spin-glass ordering at finite temperature.