Non-linear modes and statistical mechanics of a classical Heisenberg chain with two anisotropies

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Abstract
The authors investigate the relevance of soliton modes for the statistical mechanics of a classical Heisenberg chain with two single-ion anisotropies-a model that has two continuous degrees of freedom and allows one to treat exactly the crossover between broken Heisenberg and planar symmetries. Starting from exact soliton solutions as given by Sklyanin the authors discuss the two branches of the soliton spectrum, small vibrations in the presence of solitons and the stability of solitons. They show that the statistical mechanics of this chain as obtained from the transfer integral method is reproduced exactly by the phenomenological approach using solitons and phonons. The relevance of the model for the properties of the easy-plane antiferromagnetic chain in an external magnetic field is discussed.