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

Abstract

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 $T\to \infty$, $C_{11}(t)\propto t^{-N}$ for $Jt>>1$. At low $T$, the antiferromagnetic $C_{11}(t)$ is a simple function of $(JT{)}^{1/2}t$, 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 $T\to \infty$, the near-neighbor correlation functions of $N$-spin classical Heisenberg rings are simply obtained from these results.

4 pages, 4 figures, submitted to PRL

References in corpus (1)

• Zero-field Time Correlation Functions of Four Classical Heisenberg Spins on a Ring

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