LONG-TIME TAILS IN THE DYNAMICS OF THE SPATIALLY INHOMOGENEOUS MAGNETIZATION OF DIMERIZED ISOTROPIC XY CHAINS FOR SPIN S=1 2/

Exact results for the dynamics of the spatially inhomogeneous magnetiz ation (SIM) in the one-dimensional dimerized isotropic XY model are ob tained, and the long-time behavior of SIM is considered in detail. It is shown that in the asymptotic limit t --> infinity, the time depende nce of SIM can be represented as a sum of several components oscillati ng at different frequencies. Amplitudes of these components decrease a ccording to the (t/tau)(-v) power law. It is shown that both, the inve rse of the time scale tau(-1) and the exponent v, have critical-like b ehavior with respect to the wave-vector Q characterizing the spatial i nhomogeneity of the initial state. The value of tau(-1) goes to zero a t \Q\ --> Q(ci), where Q(ci) (i = 1, 2, 3) are critical values of Q de termined by parameters of the main Hamiltonian only. Just at points Q( c1), Q(c2), the exponent v changes its value discontinuously from v = 1/2 to v = 1/4. This effect is very similar to the critical slowing do wn phenomena in phase transitions. Due to the long-time tails in the r elaxation process, we critically discuss the validity of the spin temp erature assumption in spin systems.