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 nif. Our approach is primarily dynamical, and is based on the convergence o f sigma(t), a zero-temperature dynamical process with flips of lattice anim als up to size M and starting from a deep quench, to a metastable limit sig ma(infinity). 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 rel ations to thermodynamic states. For example, we show that their overlap dis tribution is a delta function at zero. We also define a dynamics for M = in finity, which provides a potential tool for investigating ground state stru cture. [S1063-651X(99)07111-1].