Subextensive Singularity in the 2D ± J Ising Spin Glass

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Abstract

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 T5.33 ± 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 $$ = 2 - α, even though Tc = 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.

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