Anomalous Fluctuations in Phases with a Broken Continuous Symmetry

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 [Formula presented]. In dimensions [Formula presented], the variance of the extensive spontaneous magnetization scales as [Formula presented] with the system size [Formula presented], independent of the order parameter dynamics. The anomalous scaling is a consequence of the [Formula presented] 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 [Formula presented]. 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.