Upward renormalization of the antiferromagnetic mode in the paramagnetic phase of CsMnBr_3

We study the renormalization of the excitation energy in the paramagnetic phase of a hexagonal Heisenberg model with strong exchange interaction along the c axis and weak exchange interaction in the c plane by a Green function approach. We compare our results with experiments of inelastic neutron scattering on CsMnBr3, a quasi-one-dimensional antiferromagnet with S=5/2. The upward renormalization of the antiferromagnetic mode observed in a neutron scattering experiment in the paramagnetic phase is obtained by our approach which is based on the absence of long-range order. On the contrary, downward renormalization of the long-wavelength modes is predicted in agreement with experimental data on CsMnBr3.