It is believed that the $\pm J$ Ising spin-glass does not order at finite
temperatures in dimension $d=2$. However, using a graphical representation and
a contour argument, we prove rigorously the existence of a finite-temperature
phase transition in $d\geq 2$ with $T_c \geq 0.4$. In the graphical
representation, the low-temperature phase allows for the coexistence of
multiple infinite clusters each with a rigidly aligned spin-overlap state.
These clusters correlate negatively with each other, and are entropically
stable without breaking any global symmetry. They can emerge in most graph
structures and disorder measures.
