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We compute the exact partition function of 2d Ising spin glasses with binarycouplings. In these systems, the ground state is highly degenerate and isseparated from the first excited state by a gap of size 4J. Nevertheless, wefind that the low temperature specific heat density scales as exp(-2J/T),corresponding to an ``effective'' gap of size 2J; in addition, an associatedcross-over length scale grows as exp(J/T). We justify these scalings via thedegeneracy of the low-lying excitations and by the way low energy domain wallsproliferate in this model

physical review letters

Critical Thermodynamics of the Two-Dimensional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mo>±</mml:mo><mml:mi>J</mml:mi></mml:math>Ising Spin Glass

Critical Thermodynamics of the Two-Dimensional±JIsing Spin Glass