LAUSR

We calculate the dynamic structure factor S(k, ω) in the paramagnetic regime of quantum Heisenberg ferromagnets for temperatures T close to the critical temperature Tc using our recently developed functional renormalization group approach to quantum spin systems. In d = 3 dimensions we find that for small momenta k and frequencies ω the dynamic structure factor assumes the scaling form S(k, ω) = (τTG(k)/π)Φ(kξ, ωτ), whereG(k) is the static spin-spin correlation function, ξ is the correlation length, and the characteristic time-scale τ is proportional to ξ. We explicitly calculate the dynamic scaling function Φ(x, y) and find satisfactory agreement with neutron scattering experiments probing the critical spin dynamics in EuO and EuS. Precisely at the critical point where ξ =∞ our result for the dynamic structure factor can be written as S(k, ω) = (πωk) TcG(k)Ψc(ω/ωk), where ωk ∝ k. We find that Ψc(ν) vanishes as ν−13/5 for large ν, and as ν for small ν. While the large-frequency behavior of Ψc(ν) is consistent with calculations based on mode-coupling theory and with perturbative renormalization group calculations to second order in = 6−d, our result for small frequencies disagrees with previous calculations. We argue that up until now neither experiments nor numerical simulations are sufficiently accurate to determine the low-frequency behavior of Ψc(ν). We also calculate the low-temperature behavior of S(k, ω) in oneand two dimensional ferromagnets and find that it satisfies dynamic scaling with exponent z = 2 and exhibits a pseudogap for small frequencies.