Finite-size scaling of the time-dependent structure factor in the one-dimensional Glauber model

We study the time-dependent structure factor of the one-dimensional Glauber model upon instantaneous cooling. Results obtained earlier by Reiss, Mazenko and Widom, and Bray, are linked together. Next, finite-size scaling in the limit of zero temperature, long times, small wave vectors, and large systems, is established. The scaling function is compared with numerical simulation results obtained by Viñals and Jasnow in the case of a two-dimensional Glauber model quenched into the region of phase separation.