LA Probability Forum

I will present the solutions to two open problems about the Edwards-Anderson model of short-range spin glasses (in all dimensions). First, I will show that the ground state is sensitive to small perturbations of the disorder, in the sense that a small amount of noise gives rise to a new ground state that is nearly orthogonal to the old one with respect to the site overlap inner product. Second, I will prove that one can overturn a macroscopic fraction of the spins in the ground state with an energy cost that is negligible compared to the size of the boundary of the overturned region - a feature that is believed to be typical of spin glasses but clearly absent in ferromagnets. Together, these comprise the first mathematical proof of glassy behavior in a short-range spin glass model.