Journal of Statistical Physics, VoL 65, Nos. 5/6, 1991, p. 1235-1246.
The relationship between the one-dimensional kinetic Ising model at zero
temperature and diffusion-annihilation in one dimension is studied. Explicit
asymptotic results for the average domain size, average magnetization squared,
and pair-correlation function are derived for the Ising model, for arbitrary
initial magnetization. For the case of zero initial magnetization (m0 = 0), a num-
ber of recent exact results for diffusion-annihilation with random initial condi-
tions are obtained. However, for the case mo not equal to zero, the asymptotic
behavior turns out to be different from diffusion-annihilation with random
initial conditions and at a finite density. In addition, in contrast to the case of
diffusion-annihilation, the domain-size distribution scaling function h(x) is
found to depend nontrivially on the initial magnetization. The origin of these
differences is clarified and the existence of nontrivial correlations in the initial
wall distribution for finite initial magnetization is found to be responsible for
these differences. Results of Monte Carlo simulations for the domain size
distribution function for different initial magnetizations are also presented.