Zero-field time correlation functions of four classical Heisenberg spins on a ring - art. no. 104424

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 explici tly for the time evolution of each of the spins. Exact triple integral repr esentations are derived for the auto, near-neighbor, and next-nearest-neigh bor 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 int egrals. At low temperatures, the Fourier transform functions explicitly dem onstrate the presence of magnons. Our exact results for the infinite-temper ature correlation functions in the long-time asymptotic limit differ, quali tatively from those obtained assuming diffusive spin dynamics. Whether such explicitly nonhydrodynamic behavior would be maintained for large-N rings is discussed.