  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.
