Recursive dynamics in an asymmetrically constrained kinetic Ising chain

For a hierarchically constrained kinetic Ising chain it is shown that the p rocess 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 th e spin autocorrelation Function is calculated analytically for N = 2 and 4 and numerically for N = 4 and 8. From the conjectured behaviour for arbitra ry N it is concluded that the mean spin relaxation time tau(infinity) on th e infinite chain for c --> 0 diverges more strongly than any positive power of(1/c). (C) 1999 Published by Elsevier Science B.V. All rights reserved.