A generalization of the Mermin and Wagner's theorem for a one-dimensional integer-spin chain with free boundary condition characterized by a spin Hamiltonian containing, in addition to the bilinear exchange term of the Heisenberg type, the biquadratic exchange term is given. It is demonstrated, by means of quantum statistical arguments based on the Bogoliubov inequality, that the law governing the vanishing of the magnetization with the ordering field is the same as in the bilinear case when both bilinear and biquadratic exchange are taken into account. These results are compared with the ones obtained by treating the exchange terms within the mean-field theory where a different vanishing power law of the magnetization is followed. The Goldstone theorem is proved for this spin Hamiltonian. A comparison with the Mermin and Wagner's results for the two-dimensional case is also performed. -- Presentazione poster by R. Zivieri - Conferenza internazionale
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