Classical one-dimensional Heisenberg magnet in an applied field

Abstract

We present theoretical results for the thermodynamic properties and time-independent spin-spin correlation functions for the classical Heisenberg magnetic chain in an applied magnetic field. The calculations are performed by numerical solution of the transfer-matrix integral equation. In addition, approximate variational procedures and low-temperature expansions yield some analytic results. The procedures used are applicable to any near-neighbor interaction for classical spins in a linear chain. The most unusual behavior found is for antiferromagnetic coupling, where the specific heat shows oscillations as a function of field, and the longitudinal uniform susceptibility and the transverse staggered susceptibility increase with field for low fields.