LOW-TEMPERATURE RELAXATION IN THE ONE-DIMENSIONAL ISING-MODEL

The decay of the spin-spin time correlation functions in a one-dimensi onal Ising model with Glauber dynamics is studied. In the low-temperat ure limit, an asymptotically valid continuous space equation is derive d. It is a modified diffusion equation with a purely exponential relax ation term. Its solution leads to an exact Cole-Davison behavior of th e spin autocorrelation in the frequency domain, while in the time desc ription a Kohlrausch-Williams-Watts (KWW) function followed by an expo nential decay is obtained. The exponent of the KWW function, analytica lly derived, is 1/2, and not 0.63, as has been reported in the literat ure.