Spectral density method for an anisotropic linear chain

The spectral density method is used to study the thermodynamic properties of an anisotropic antiferromagnetic Heisenberg linear chain in an external magnetic field. Insecond order approximation without the decoupling procedure for the two particle correlation function, we are able to obtain many results in terms of both the temperature and the magnetic field for different values of the anisotropy parameter. The ground state of the model is investigated and the singular behaviour of some thermodynamic quantities near the critical field is determined. In particular, explicit analytical solutions are given for small anisotropy parameters. Our results are compared with the ones obtained by means of other methods and some exact results are reproduced.