Low-temperature thermodynamics and correlation functions for a classical Heisenberg chain with two anisotropies

The authors derive the thermodynamics and the static correlation functions for the classical Heisenberg chain with the anisotropies within a low-temperature steepest-descent approach. As regards the thermodynamics, they find agreement with transfer matrix and 'ideal-gas' phenomenological results. For the longitudinal correlation function the authors find an antiferromagnetic-type behaviour with a correlation length inversely proportional to the domain wall density. The transverse in-plane correlation function exhibits a damped oscillatory behaviour due to domain-wall-spin interference. The transverse out-of-plane correlations, on the other hand, are exponentially damped with the correlation length increasing as the easy-axis limit is approached.