  Direct measurements of the spin glass correlation function $G(R)$ for
Gaussian and bimodal Ising spin glasses in dimension two have been carried out
in the temperature region $T \sim 1$. In the Gaussian case the data are
consistent with the known anomalous dimension value $\eta \equiv 0$. For the
bimodal spin glass in this temperature region $T > T^{*}(L)$, well above the
crossover $T^{*}(L)$ to the ground state dominated regime, the effective
exponent $\eta$ is clearly non-zero and the data are consistent with the
estimate $\eta \sim 0.28(4)$ given by McMillan in 1983 from similar
measurements. Measurements of the temperature dependence of the Binder cumulant
$U_{4}(T,L)$ and the normalized correlation length $\xi(T,L)/L$ for the two
models confirms the conclusion that the 2D bimodal model has a non-zero
effective $\eta$ both below and above $T^{*}(L)$. The 2D bimodal and Gaussian
interaction distribution Ising spin glasses are not in the same Universality
class.
