The one-dimensional classical planar model in an applied magnetic field

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Abstract
The author presents calculations, using a transfer matrix method, for the one-dimensional classical planar model in an applied magnetic field. In particular, the correlation lengths for spin fluctuations parallel and transverse to the applied field are calculated. For low temperatures and antiferromagnetic coupling, these show behaviour characterising a crossover from planar to Ising-like behaviour, corresponding to a lowering of the effective spin dimensionality by the applied field. For low temperatures it is shown that the crossover can be characterised by universal scaling functions. The results are shown to be in good agreement with experimental values, obtained by quasi-elastic neutron scattering from TMMC which, for low temperatures, is expected to be well described by the planar model.