Nature of Ground State Incongruence in Two-Dimensional Spin Glasses
  We rigorously rule out the appearance of multiple domain walls between ground states in 2D Edwards-Anderson Ising spin glasses (with periodic boundary conditions and, e.g., Gaussian couplings). This supports the conjecture that there is only a single pair of ground states in these models. 
C.M. Newman (Courant Institute of Mathematical Sciences, New York   University), D.L. Stein (Departments of Physics and Math...