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The statistics of the ground-state and domain-wall energies for thetwo-dimensional random-bond Ising model on square lattices with independent,identically distributed bonds of probability $p$ of $J_{ij}= -1$ and $(1-p)$ of$J_{ij}= +1$ are studied. We are able to consider large samples of up to$320^2$ spins by using sophisticated matching algorithms. We study $L \times L$systems, but we also consider $L \times M$ samples, for different aspect ratios$R = L / M$. We find that the scaling behavior of the ground-state energy andits sample-to-sample fluctuations inside the spin-glass region ($p_c \le p \le1 - p_c$) are characterized by simple scaling functions. In particular, thefluctuations exhibit a cusp-like singularity at $p_c$. Inside the spin-glassregion the average domain-wall energy converges to a finite nonzero value asthe sample size becomes infinite, holding $R$ fixed. Here, large finite-sizeeffects are visible, which can be explained for all $p$ by a single exponent$\omega\approx 2/3$, provided higher-order corrections to scaling are included.Finally, we confirm the validity of aspect-ratio scaling for $R \to 0$: thedistribution of the domain-wall energies converges to a Gaussian for $R \to 0$,although the domain walls of neighboring subsystems of size $L \times L$ arenot independent.Comment: 11 pages with 15 figures, extensively revise

physical review. b, condensed matter and materials physics

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Ground-state and domain-wall energies in the spin-glass region of the two-dimensional±Jrandom-bond Ising model