We study domain walls in 2d 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 df of domain walls, which describes via
\simL^{d_f} the growth of the average domain-wall length with %%
systems size L×L. %% 20.07.07 OM %% Exploring systems up to L=320 we
yield df=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 df=1.095(2) and a (lower) estimate df=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 df, 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.Comment: 8 pages, 8 figures, submitted to Phys. Rev. B; v2: shortened versio