Dynamics of fluctuations in the ordered phase of kinetic Ising models

Correlation functions q(t)=〈Sₓ(0)Sₓ(t)〉-〈Sₓ〉² and their momentum space expansions are studied in computer simulations of d-dimensional Glauber models below Tc (d=2, 3, and 4). For d≥3 the functions 〈 ̃ \~Sₖ(0) ̃ \~S_-k(t)〉c decay exponentially and the relaxation-time spectrum is bounded, implying the asymptotically exponential $q(t)$, but that asymptotic form is far beyond any observable regime. For $d=2$, 〈 ̃ \~Sₖ(0) ̃ \~S_-k(t)〉c decays nonexponentially for all k indicating a nonexponential asymptotic form of $q(t)$. In all cases the observable preasymptotic form of $q(t)$ can be approximated by Kohlrausch decay exp[-(λt)^β], 0<β<1.