Exact time correlation functions for N classical Heisenberg spins in the 'squashed' equivalent neighbour model

We present exact integral representations of the time-dependent spin–spin correlation functions for the classical Heisenberg N-spin ‘squashed’ equivalent neighbour model, in which one spin is Heisenberg exchange-coupled with strength J1 to the other N − 1 spins, each of which is Heisenberg exchangecoupled with strength J2 to the remaining N − 2 spins. As the temperature T →∞ , we calculate exactly the long-time asymptotic behaviour of the correlation functions for arbitrary N, and compare our results with those obtained for three spins on an isosceles triangle. At low T ,t heN spins oscillate in four modes, one of which is a central peak for a semi-infinite range of J2/J1 values. These results differ qualitatively from those obtained for the N-spin equivalent neighbour model and the four-spin ring. Detailed numerical evaluations of the behaviour of four spins on a squashed tetrahedron are presented, including specific predictions relevant for neutron scattering experiments on Fe4. In particular, two prominent peaks in the Fourier transform of the correlation functions are predicted for Fe4, the positions of which provide a measure of J1 and J2.