Statistical mechanics of a turbulent ferromagnetic medium

Abstract

Statistical equations for the response of a fully or partially demagnetized ferromagnetic insulator to a time-varying magnetic field are proposed. The theory is based on the classical dynamical equation for a ferromagnetic continuum, including exchange, anisotropy, and magnetic dipole effects. A set of statistical equations couples the rates of change of the average magnetization, of Green's functions and of second-order two-time correlation functions constructed from space-Fourier components of the magnetization. The set is closed by making use of the direct-interaction approximation introduced by Kraichnan in the theory of homogeneous fluid turbulence. It is shown that the approximate equations conserve energy and the average spontaneous magnetization squared. Static equilibrium properties are derived in preparation for attacking dynamic problems. In equilibrium, the spectral distribution of magnetization in wave-vector space consists of a narrow peaked region about the origin of wave-vector space plus a spread-out background. The peaked region represents the statistical analogue of ordinary domain structure and has negligible energy content, while the background represents an equipartition of the available internal energy among all Fourier components. General properties of the statistical equations indicate that they may be meaningful in connection with problems not involving pronounced anisotropy of the spectrum. © 1967 The American Institute of Physics.