Metastable states in spin glasses and disordered ferromagnets

We study analytically M-spin-flip stable states in disordered short-ranged Ising models (spin glasses and ferromagnets) in all dimensions and for all M. Our approach is primarily dynamical, and is based on the convergence of [Formula Presented] a zero-temperature dynamical process with flips of lattice animals up to size M and starting from a deep quench, to a metastable limit [Formula Presented] The results (rigorous and nonrigorous, in infinite and finite volumes) concern many aspects of metastable states: their numbers, basins of attraction, energy densities, overlaps, remanent magnetizations, and relations to thermodynamic states. For example, we show that their overlap distribution is a [Formula Presented] function at zero. We also define a dynamics for [Formula Presented] which provides a potential tool for investigating ground state structure.