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

Abstract

A model relevant for the study of certain molecular magnets is the ring of N=4 classical spins with equal near-neighbor isotropic Heisenberg exchange interactions. Assuming classical Heisenberg spin dynamics, we solve explicitly for the time evolution of each of the spins. Exact triple integral representations are derived for the auto, near-neighbor, and next-nearest-neighbor time correlation functions for any temperature. At infinite temperature, the correlation functions are reduced to quadrature. We then evaluate the Fourier transforms of these functions in closed form, which are double integrals. At low temperatures, the Fourier transform functions explicitly demonstrate the presence of magnons. Our exact results for the infinite temperature correlation functions in the long-time asymptotic limit differ qualitatively from those obtained assuming diffusive spin dynamics. Whether such explicitly non-hydrodynamic behavior would be maintained for large-N rings is discussed.

18 pages, 21 figures

References in corpus (1)

• Single-Crystal High-Frequency EPR Investigation of a Tetranuclear Iron(III) Single-Molecule Magnet

Cited by in corpus (8)

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• Theory of high-symmetry tetramer single molecule magnets
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• Exact Time Autocorrelation Function of the N-Spin Classical Heisenberg Equivalent Neighbor Model
• Thermodynamics of the spin square
• Exact time correlation functions for N classical Heisenberg spins in the `squashed' equivalent neighbor model
• Thermodynamics of the classical spin triangle