Subextensive Singularity in the 2D ± <Emphasis Type="Italic">J</Emphasis> Ising Spin Glass

The statistics of low energy states of the 2D Ising spin glass with +1 and −1 bonds are studied for L × L square lattices with L≤ 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 ± 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 ν = 2 − α, 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. PACS numbers: 75.10.Nr, 75.40.Mg, 75.60.Ch, 05.50.+q