Random Fields, Topology, and the Imry-Ma Argument

We consider an n-component fixed-length order parameter interacting with a weak random field in d = 1, 2, 3 dimensions. Relaxation from the initially ordered state and spin-spin correlation functions are studied on lattices containing hundreds of millions of sites. At n <= d the presence of topological defects leads to strong metastability and glassy behavior, with the final state depending on the initial condition. At n = d + 1, when topological structures are nonsingular, the system possesses a weak metastability. At n > d + 1, when topological objects are absent, the final, lowest-energy state is independent of the initial condition. It is characterized by the exponential decay of correlations that agrees quantitatively with the theory based upon the Imry-Ma argument.