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 \(T\to\infty\), \(C_{11}(t)\propto t^{-N}\) for \(Jt>>1\). At low \(T\), the antiferromagn...

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Bibliographic Details
Published inarXiv.org
Main Authors Klemm, Richard A, Ameduri, Marco
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 13.12.2001
Subjects
Antiferromagnetism
Autocorrelation functions
Correlation analysis
Equivalence
Ferromagnetism
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Summary: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 \(T\to0\). We conjecture that as \(T\to\infty\), the near-neighbor correlation functions of \(N\)-spin classical Heisenberg rings are simply obtained from these results.
ISSN:2331-8422
DOI:10.48550/arxiv.0112236