Scalings of domain wall energies in two dimensional Ising spin glasses

We study domain wall energies of two dimensional spin glasses. The scaling of these energies depends on the model's distribution of quenched random couplings, falling into three different classes. The first class is associated with the exponent theta =-0.28, the other two classes have theta = 0, as can be justified theoretically. In contrast to previous claims, we find that theta=0 does not indicate d=d_l but rather d <= d_l, where d_l is the lower critical dimension.