Dynamics of a system with three-spin interection in the Gaussian fluctuating local field approximation

For a spin system with the effective Hamiltonian induced by a strong rf field the dependence of temporal correlation functions (TCF) on the correlation time of fluctuating resonance frequency is studied. In the Anderson's approach the two-spin effective interaction creates the Gaussian fluctuating local field in resonance frequency meanwhile the three-spin one creates this field squared and another Gaussian random variable. The equations allowing to compute TCF for any Gaussian process with arbitrary correlation function are obtained. Verious limiting cases are discussed. The computation is fulfilled for the noises with exponential and Gaussian forms of correlation function. It is shown that the properties of TCF in the system with three-spin interaction differ from the well-known ones in the systems with two-spin interaction.