Out-of-equilibrium 2D Ising spin glass: almost, but not quite, a free-field theory

We consider the spatial correlation function of two-dimensional Ising spin glass under out-of-equilibrium conditions. We pay special attention to the scaling limit reached upon approaching zero temperature. The field-theory of a non-interacting field makes a surprisingly good job of describing the spatial shape of the correlation function of the out-of-equilibrium Edwards- Anderson Ising model in two dimensions.