Stretched exponential decay of the spin-correlation function in the kinetic Ising model below the critical temperature

The equilibrium long-time behavior of the autocorrelation function 〈$S_i$(0)$S_i$(t)${〉}_c$ =〈$S_i$(0)$S_i$(t)〉-〈$S_i$ ${〉}^2$ of the ith spin $S_i$ in the kinetic Ising model is studied below the critical temperature. Based on the expansion of the correlation function into exponentially relaxing modes and on the fact that relaxation rates of these modes constitute a continuous spectrum from zero, it is argued that 〈$S_i$(0)$S_i$(t)${〉}_c$ decays stretched exponentially as exp[-${\mathrm{Dt}}^{\left(d\mathrm{-}1\right)/(d+1)}$] in the d-dimensional system. The results of Monte Carlo simulation on the square lattice support the stretched-exponential decay.