An analysis is given of numerical simulation data to size L = 128 on the archetype square lattice Ising spin glasses (ISGs) with bimodal (+/- J) and Gaussian interaction distributions. It is well established that the ordering temperature of both models is zero. The Gaussian model has a nondegenerate ground state and thus a critical exponent. = 0, and a continuous distribution of energy levels. For the bimodal model, above a size-dependent crossover temperature T *(L) there is a regime of effectively continuous energy levels; below T *(L) there is a distinct regime dominated by the highly degenerate ground state plus an energy gap to the excited states. T *(L) tends to zero at very large L, leaving only the effectively continuous regime in the thermodynamic limit. The simulation data on both models are analyzed with the conventional scaling variable t = T and with a scaling variable tau(b) = T-2 /(1 + T 2) suitable for zero-temperature transition ISGs, together with appropriate scaling expressions. The data for the temperature dependence of the reduced susceptibility x(tau(b), L) and second moment correlation length xi(tau(b), L) in the thermodynamic limit regime are extrapolated to the tau(b) = 0 critical limit. The Gaussian critical exponent estimates from the simulations, eta= 0 and nu= 3.55(5), are in full agreement with the well-established values in the literature. The bimodal critical exponents, estimated from the thermodynamic limit regime analyses using the same extrapolation protocols as for the Gaussian model, are eta= 0.20(2) and nu= 4.8(3), distinctly different from the Gaussian critical exponents.
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