The bimodal Ising spin glass in dimension two : the anomalous dimension $\eta$

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.