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Anomalous fluctuations in phases with a broken continuous symmetry

W. Zwerger
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Abstract

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-ω^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.

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W. Zwerger. 2004-01-26. Anomalous fluctuations in phases with a broken continuous symmetry. https://doi.org/10.1103/physrevlett.92.027203

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