Exact Time Autocorrelation Function of the N-Spin Classical Heisenberg Equivalent Neighbor Model

We reduce the autocorrelation function $C_{11}(t)$ of the equivalent neighbor model of $N$ classical spins exhibiting Heisenberg dynamics and exchange coupling $J$ to quadrature. As the temperature $T\to \mathrm{\infty }$, $C_{11}(t)\propto t^{-N}$for$Jt>>1$\mathrm{.}Atlow$T$,theantiferromagnetic$C_{11}(t)$ is a simple function of $(JT{)}^{1\mathrm{/}2}t$, exhibiting strong frustration, but the ferromagnetic $C_{11}(t)$ oscillates in a single mode the frequency of which approaches $NJ$ as $T\to 0$. We conjecture that as $T\to \mathrm{\infty }$, the near-neighbor correlation functions of $N$-spin classical Heisenberg rings are simply obtained from these results.