Rigorous Bounds for Time-Dependent Spin Correlation Functions

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Abstract
The recently developed method of constructing rigorous upper and lower bounds for time-dependent correlation functions is applied to systems of interacting spins. Rigorous bounds are calculated for the free-induction-decay curves of a cubic lattice of dipolar-coupled classical spins on the basis of the exact first eight moments of the corresponding absorption curves. The bounds are shown to be in good agreement with the curves obtained from computer experiments. A calculation of bounds for Abragam's model function gives an indication of the number of moments necessary for a determination of the various parts of the decay curves. Moment theory is applied to explain the negative portions of the absorption curves derived from expansion theories for dipolar-coupled spin systems. Rigorous bounds are also calculated for the autocorrelation function of the linear Heisenberg magnet of spin-1/2 at infinite temperature from the first ten initial time derivatives of the correlation function.