Dynamics of a transverse Ising model with four-spin interactions

We report the first study of the dynamics of a transverse Ising model with four-spin interactions. We consider finite chains of increasing size in order to determine the time-dependent correlation function as well as the longitudinal relaxation function of the infinite chain. Up to 8 exact 5 approximate moments of the infinite chain were also obtained. The correlation function is oscillatory for large values of the transverse field and is monotonically decreasing for small values of the transverse field. The system undergoes a crossover from a collective mode excitation regime to a central mode type of dynamics as the strenght of field is lowered. The present model does not allow Gaussian decay for the correlation function.