  The statistics of domain walls for ground states of the 2D Ising spin glass
with +1 and -1 bonds are studied for $L \times L$ square lattices with $L \le
20$, and $x$ = 0.25 and 0.5, where $x$ is the fraction of negative bonds, using
periodic and/or antiperiodic boundary conditions. Under these conditions,
almost all domain walls have an energy $E_{dw}$ equal to 0 or 4. The
probability distribution of the entropy, $S_{dw}$, is found to depend strongly
on $E_{dw}$. The results for $S_{dw}$ when $E_{dw} = 4$ agree with the
prediction of the droplet model. Our results for $S_{dw}$ when $E_{dw} = 0$
agree with those of Saul and Kardar. In addition, we find that the
distributions do not appear to be Gaussian in that case. The special role of
$E_{dw} = 0$ domain walls is discussed, and the discrepancy between the
prediction of Amoruso, Hartmann, Hastings and Moore and the result of Saul and
Kardar is explained.
