Longitudinal relaxation spectra of the transverse Ising model close to Tc

The correlative effects of the nature of the interaction and of the method of calculation on the shape of the longitudinal relaxation function (LRF) for the transverse Ising model are analysed. The LRF is calculated in two ways: (i) its continued fraction representation within the three pole approximation (TPA); and (ii) the resolution of kinetic equations derived for the correlation functions beyond the random phase approximation (RPA). The effects of the nature of the interaction on the LRF spectral characteristics are investigated using an interaction made of three variable contributions: uniaxial dipolar, isotropic infinite range and anisotropic nearest-neighbour interactions. Contrary to the TPA, the kinetic-equation-method (KEM) leads to LRF's exhibiting a three peak structure for every q-value except q = 0 (q = 0⊥ if the interaction is of dipolar nature) whatever the interaction. The approximations underlying both methods are specified and discussed. Comments on recent neutron scattering experiments on Li TbpY1-pF4 by Youngblood et al. are made.