Overlap interfaces in hierarchical spin-glass models

We discuss interfaces in spin glasses. We present new theoretical results and a numerical method for characterizing overlap interfaces and the stability of the spin-glass phase in extended disordered systems. We use this definition to characterize the low temperature phase of hierarchical spin-glass models. We use the replica symmetry breaking theory to evaluate the cost for an overlap interface, which in these models is particularly simple. A comparison of our results from numerical simulations with the theoretical predictions shows good agreement.