The autocorrelation function, C(t)= Si(0)Si(t)Si2 (0), of Ising spins in an ordered phase (T<Tc) is studied via a droplet model. Only noninteracting spherical droplets are considered. The Langevin equation for droplet fluctuations is studied in detail. The relaxation-rate spectra for the corresponding Fokker-Planck equation are found to be (1) continuous from zero for dimension d=2, (2) continuous with a finite gap for d=3, and (3) discrete for d4. These spectra are different from the gapless form assumed by Takano, Nakanishi, and Miyashita for the kinetic Ising model. The asymptotic form of C(t) is found to be exponential for d3 and stretched exponential with the exponent =1/2 for d=2. Our results for C(t) are consistent with the scaling argument of Huse and Fisher, but not with Ogielskis Monte Carlo simulations.
All Science Journal Classification (ASJC) codes
- Atomic and Molecular Physics, and Optics