A domain theory for linear and nonlinear aging effects in spin glasses

We present a theory of aging in spin glasses subjected to a time-dependent temperature and external magnetic field. An arbitrary nonequilibrium spin glass state is imagined to be decomposable into a collection of « (T 1, H1)-domains » (for any pair (T1, H1)) through a comparison of this state to an equilibrium state at a temperature T1 and in a field H1 . The theory postulates a time evolution for the domains (comprising both growth and breakup), as well as an equation for the magnetic relaxation within a domain. Of crucial importance is the interplay between two characteristic lengths : i) the time-dependent linear size of a domain, and ii) an overlap length l (ΔT, ΔH) ; the latter indicates up until which length scale two thermodynamic equilibrium states differing by ΔT and ΔH are indistinguishable. We show that the theory explains a variety of experimental aging effects as have been observed in particular by Refregier et al. and by Lundgren et al.