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At zero temperature, two-dimensional Ising spin glasses are known to fall into several universality classes. Here we consider the scaling at low but non-zero temperature and provide numerical evidence that $\eta \approx 0$ and $\nu \approx 3.5$ in all cases, suggesting a unique universality class. This algebraic (as opposed to exponential) scaling holds in particular for the $\pm J$ model, with or without dilutions and for the plaquette diluted model. Such a picture, associated with an exceptional behavior at T=0, is consistent with a real space renormalization group approach. We also explain how the scaling of the specific heat is compatible with the hyperscaling prediction.

The ground state and low T behavior of two-dimensional spin systems with discrete binary couplings are subtle but can be analyzed using exact computations of finite volume partition functions. We first apply this approach to Villain's fully frustrated model, unveiling an unexpected finite size scaling law. Then we show that the introduction of even a small amount of disorder on the plaquettes dramatically changes the scaling laws associated with the T=0 critical point., Comment: Latex with 3 ps figures. Last version

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