Low-temperature relaxation in the one-dimensional Ising model

The decay of the spin-spin time correlation functions in a one-dimensional Ising model with Glauber dynamics is studied. In the low-temperature limit, an asymptotically valid continuous space equation is derived. It is a modified diffusion equation with a purely exponential relaxation term. Its solution leads to an exact Cole-Davison behavior of the spin autocorrelation in the frequency domain, while in the time description a Kohlrausch-Williams-Watts (KWW) function followed by an exponential decay is obtained. The exponent of the KWW function, analytically derived, is 1/2, and not 0.63, as has been reported in the literature.