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The statistics of low energy states of the 2D Ising spin glass with +1 and -1bonds 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/orantiperiodic boundary conditions. The behavior of the density of states nearthe ground state energy is analyzed as a function of $L$, in order to obtainthe low temperature behavior of the model. For large finite $L$ there is arange 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 thatthis model probably obeys the ordinary hyperscaling relation $d \nu = 2 -\alpha$, even though $T_c = 0$. The existence of the subextensive behavior isattributed to long-range correlations between zero-energy domain walls, andevidence of such correlations is presented.Comment: 13 pages, 7 figures; final version, to appear in J. Stat. Phy

Subextensive Singularity in the 2D ± J Ising Spin Glass