NONEQUILIBRIUM STATISTICAL-MECHANICS OF THE SPIN-1/2 VANDERWAALS MODEL .2. AUTOCORRELATION FUNCTION OF A SINGLE SPIN AND LONG-TIME TAILS

The autocorrelation function of a single spin [s(t).s(O)] has been obtained from the time-evolution solutions given in the preceding paper by carrying out the ensemble averages explicitly. Slow decay is found in the transverse component and only at high temperatures (T > T(c)). The exponent kappa, where [s(x)(t)s(x)(O)] approximately t-kappa, as t --> infinity, is found to depend discontinuously on the spin-spin interaction strength R = J(z)/J: kappa = 2 if R = O, kappa = 3 if 0 < R less-than-or-equal-to 2 (R not-equal 1), kappa = infinity if R = 1, and kappa = infinity if R > 2. Slow decay in this model is attributed to nondimensional effects, e.g., cooperatively. Physical and mathematical mechanisms of the slow decay are described.