Spin-liquid phase in the pyrochlore anti-ferromagnet

Correlation functions (CFs) of the classical Heisenberg anti-ferromagnet on the pyrochlore lattice are studied by solving exactly the infinite-component spin-vector model. As in many fully frustrated lattices, the constraint due to the minimization of the energy and the particular structure based on corner-sharing tetrahedra both contribute to the creation of local degrees of freedom. The resulting degeneracy destroys any magnetic order at all temperatures and we obtain no sign of criticality, even at T = 0. Calculated neutron-scattering cross sections have their maxima beyond the first Brillouin zone and reproduce experimental results obtained on Y(Sc)Mn-2 and CsCrNiF6 as well as theoretical predictions previously obtained by classical Monte Carlo simulations. Evidences for thermal and spatial decoupling of the magnetic modes are found so that the magnetic fluctuations in this system can be approximated by S(q, T) approximate to f(q)h(T).