Approximate dynamical eigenmodes of the Ising model with local spin-exchange moves

We establish that the Fourier modes of the magnetization serve as the dynamical eigenmodes for the twodimensional Ising model at the critical temperature with local spin-exchange moves, i.e., Kawasaki dynamics. We obtain the dynamical scaling properties for these modes and use them to calculate the time evolution of two dynamical quantities for the system, namely, the autocorrelation function and the mean-square deviation of the line magnetizations. At intermediate times 1 t Lzc , where zc = 4 − η = 15/4 is the dynamical critical exponent of the model, we find that the line magnetization undergoes anomalous diffusion. Following our recent work on anomalous diffusion in spin models, we demonstrate that the generalized Langevin equation with a memory kernel consistently describes the anomalous diffusion, verifying the corresponding fluctuationdissipation theorem with the calculation of the force autocorrelation function