  The statistics of low energy states of the 2D Ising spin glass with +1 and -1
bonds are studied for $L \times L$ square lattices with $L \le 48$, and $p$ =
0.5, where $p$ is the fraction of negative bonds, using periodic and/or
antiperiodic boundary conditions. The behavior of the density of states near
the ground state energy is analyzed as a function of $L$, in order to obtain
the low temperature behavior of the model. For large finite $L$ there is a
range of $T$ in which the heat capacity is proportional to $T^{5.33 \pm 0.12}$.
The range of $T$ in which this behavior occurs scales slowly to $T = 0$ as $L$
increases. Similar results are found for $p$ = 0.25. Our results indicate that
this model probably obeys the ordinary hyperscaling relation $d \nu = 2 -
\alpha$, even though $T_c = 0$. The existence of the subextensive behavior is
attributed to long-range correlations between zero-energy domain walls, and
evidence of such correlations is presented.
