Classical one-dimensional ferromagnets in a magnetic field: Static and dynamical properties

Abstract

An interacting-spin-wave theory is presented for describing the behavior of a classical Heisenberg ferromagnetic chain in an external magnetic field. In this framework all the static and dynamical longitudinal properties can be analytically calculated by means of a nonperturbative Green's-function approach. In particular, the features of recent computer experiments showing, at intermediate wave vectors, spectra with a structure tentatively referred to as a "second-magnon" effect receive a very simple physical interpretation. It is shown that a thermally induced spin-energy coupling causes transitions between different regimes: from an ordered condition due to the field to a quasi-isotropic situation (i.e., to a "first-magnon" behavior) determined by the competitive role of the temperature. Explicit expressions for static quantities, namely longitudinal susceptibility, correlation length, and magnetization, are also given. The thermally induced crossover toward a nearly isotropic situation is found to be again present. Exact numerical calculations by the transfer-matrix method have been also performed, and an excellent agreement with the theoretical evaluation is found.