Nonlinear relaxation and ergodicity breakdown in random anisotropy spin glasses

Abstract

An exact theory of the nonlinear relaxation of a zero-dimensional magnetic anisotropy model is derived in the large- n limit where n is the number of the spin components. We consider both the “pure” and “random” case. In the random case the magnetization decays asymptotically with an inverse time power. This result is shown to be in agreement with the numerical solution of the model in the case of a large but finite n. We find a new ergodicity breaking phenomenon associated with the nonlinear relaxation in the spin glass which occurs even in the absence of replica symmetry breaking in the steady state.