Recursive dynamics in an asymmetrically constrained kinetic Ising chain

For a hierarchically constrained kinetic Ising chain it is shown that the process of spin-up propagation for small concentration c of facilitating up spins occurs recursively near the bottom of the configuration space, which has a self-similar structure. For chains with a finite number N of spins the spin autocorrelation function is calculated analytically for N=2 and 4 and numerically for N=4 and 8. From the conjectured behaviour for arbitrary N it is concluded that the mean spin relaxation time τ∞ on the infinite chain for c→0 diverges more strongly than any positive power of (1/c).