Fractal dimension of domain walls in two-dimensional Ising spin glasses

We study domain walls in two-dimensional Ising spin glasses in terms of a minimum-weight path problem. Using this approach, large systems can be treated exactly. Our focus is on the fractal dimension d(f) of domain walls, which describes via < l > similar to L-f(d) the growth of the average domain-wall length with system size LxL. Exploring systems up to L=320 we yield d(f)=1.274(2) for the case of Gaussian disorder, i.e., a much higher accuracy compared to previous studies. For the case of bimodal disorder, where many equivalent domain walls exist due to the degeneracy of this model, we obtain a true lower bound d(f)=1.095(2) and a (lower) estimate d(f)=1.395(3) as upper bound. Furthermore, we study the distributions of the domain-wall lengths. Their scaling with system size can be described also only by the exponent d(f), i.e., the distributions are monofractal. Finally, we investigate the growth of the domain-wall width with system size (roughness) and find a linear behavior.