Phase transitions, symmetry breaking and asymptotic properties of the goldstone-mode frequency

Using the nonrelativistic analogue of the Goldstone theorem and the theory of collective motion of dynamical variables developed by Mori the Goldstone-mode frequency is given in terms of the order parameter and the long-wavelength form of static susceptibilities. The damping rate is predicted to tend to zero in the long-wavelength limit as the square of the mode frequency. It is shown that the temperature dependence of the Goldstone-mode frequency is, quite generally, proportional to that of the order parameter itself. The general results are applied to the isotropic Heisenberg ferro- and antiferromagnet and superfluid helium. These results confirm predictions derived from the dynamical scaling hypothesis. © 1973.