Statistical mechanics of classical one-dimensional Heisenberg ferromagnets with single-site anisotropy

The exact analytical forms of the low-temperature thermodynamic quantities and correlation functions are obtained for classical one-dimensional Heisenberg ferromagnets with single-site anisotropy including both the systems with an easy axis and with an easy plane. The problem has been managed on the basis of the functional integral method. The calculated results have a few leading terms in series-expansion with respect to the reduced temperature, exhibiting the characteristic points borne out in the recent numerical studies. In particular, the longitudinal correlation function and susceptibility of the system with an easy axis show Ising-like behaviours and the transverse counterparts of the system with an easy plane show isotropic XY- or Heisenberg-like behaviours. Physical implications of the calculated results are also discussed.