Wavelength-dependent fluctuations in classical paramagnets in a magnetic field. II. Dynamical properties

Abstract

For pt.I see ibid., vol.9, p.3639 (1976). A description of the dynamic response of a classical paramagnet to a time and spatially varying perturbation is formulated, which takes into account coupling between the magnetization and energy densities induced by an applied magnetic field. The coupling is manifested implicitly, via thermodynamic quantities which enter the theory, and this aspect is included fully by a renormalization of the energy density. There is also an explicit modification of the dynamical equations, which is studied within the context of a generalized Langevin equation, using the formulation proposed by Mori. It is shown that a judicious choice of dynamical variables enables one to identify dynamical effects resulting from the coupling and, in particular, modifications to the frequency and width of a collective mode. In order to illustrate the consequences of this formalism, results are presented of explicit calculations for one-dimensional ferro- and antiferromagnetically coupled classical Heisenberg magnets, for which all static spin correlation functions of interest can be calculated exactly.