  The standard two-dimensional Ising spin glass does not exhibit an ordered
phase at finite temperature. Here, we investigate whether long-range correlated
bonds change this behavior. The bonds are drawn from a Gaussian distribution
with a two-point correlation for bonds at distance r that decays as
$(1+r^2)^{-a/2}$, $a>0$. We study numerically with exact algorithms the ground
state and domain wall excitations. Our results indicate that the inclusion of
bond correlations does not lead to a spin-glass order at any finite
temperature. A further analysis reveals that bond correlations have a strong
effect at local length scales, inducing ferro/antiferromagnetic domains into
the system. The length scale of ferro/antiferromagnetic order diverges
exponentially as the correlation exponent approaches a critical value, $a \to
a_c = 0$. Thus, our results suggest that the system becomes a
ferro/antiferromagnet only in the limit $a \to 0$.
