No abstract

A Green's function technique is used to study the influence of spin-phonon interactions in the Ising model with a transverse field including higher-order anharmonic terms. The renormalized phonon energy has been evaluated for the first time beyond the RPA. At low temperatures both, the anharmonic spin-phonon and phonon-phonon interactions including cubic and quadratic terms play an important role, whereas near and above the Curie temperature only the anharmonic phonon-phonon interaction contributes to the renormalization of the phonon energy.