It is shown that the Goldstone modes associated with a broken continuous symmetry lead to anomalously large fluctuations of the zero field order parameter at any temperature below $T_c$. In dimensions $2<d<4$, the variance of the extensive spontaneous magnetization scales as $L^4$ with the system size $L$, independent of the order parameter dynamics. The anomalous scaling is a consequence of the $1/q^{4-d}$ divergence of the longitudinal susceptibility. For ground states in two dimensions with Goldstone modes vanishing linearly with momentum, the dynamical susceptibility contains a singular contribution $(q^2-{\omega }^2/c^2{)}^{-1/2}$. The dynamic structure factor thus exhibits a critical continuum above the undamped spin wave pole, which may be detected by neutron scattering in the Néel phase of 2D quantum antiferromagnets.

• Received 7 April 2003

DOI:https://doi.org/10.1103/PhysRevLett.92.027203