Near optimal configurations in mean field disordered systems
arXiv:cond-mat/0307250 · doi:10.1103/PhysRevE.68.046706
Abstract
We present a general technique to compute how the energy of a configuration varies as a function of its overlap with the ground state in the case of optimization problems. Our approach is based on a generalization of the cavity method to a system interacting with its ground state. With this technique we study the random matching problem as well as the mean field diluted spin glass. As a byproduct of this approach we calculate the de Almeida-Thouless transition line of the spin glass on a fixed connectivity random graph.
13 pages, 7 figures