This paper is concerned with the nonmonotonic frequency dependence of $S(k, \ensuremath{\omega})$, the wave-number-frequency transform of the time-dependent spin-spin correlation functions for a one-dimensional Heisenberg magnet at infinite temperature, as calculated by Carboni and Richards. It is argued that this nonmonotonic feature of $S(k, \ensuremath{\omega})$ is a one-dimensional effect, and supporting evidence is presented via a phenomenological calculation of $S(k, \ensuremath{\omega})$, utilizing the equivalence of the Heisenberg chain with a fermion system.
Computer calculations of the time-dependent spin and energy correlation functions of the classical one-dimensional
XY model at infinite temperature are reported. Plots of
〈SziSzi(t)〉,
〈SziSzi+1(t)〉, $〈{\ensuremath{\epsilon}}^{i}{\ensuremath{\epsilon}}^{i}(t)〉$, and
(21)[〈SxiSxi(t)〉+〈SyiSyi(t)〉] out to times
Jt=9 are given (${\ensuremath{\epsilon}}^{i}$ is the energy-density operator and $\ensuremath{\hbar}J$ is the exchange integral). Comparison is made with the exact results for the spin-1/2
XY model. After an appropriate scaling of the exchange integral and normalization to the classical value at
t=0 the values of the spin-1/2 functions are close to the values of their classical counterparts for times up to $\mathrm{Jt}\ensuremath{\approx}4$.