Nonequilibrium statistical mechanics of the spin-1/2 van der Waals model. II. Autocorrelation function of a single spin and long-time tails

The autocorrelation function of a single spin 〈s(t){·}s(0)〉 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>Tc). The exponent {κ}, where 〈sˣ(t)sˣ(0)〉{~}t^-κ, as t{→}{∞}, is found to depend discontinuously on the spin-spin interaction strength R=Jz/J: {κ}=2 if R=0, {κ}=3 if 0R{≤}2 (R{≠}1), {κ}={∞} if R=1, and {κ}={∞} if R>2. Slow decay in this model is attributed to nondimensional effects, e.g., cooperativity. Physical and mathematical mechanisms of the slow decay are described.