Application of the functional integral method to the classical and quantum spin models

Abstract

Functional integral technique is applied to the Blume-Emery-Griffiths model (BEG) and to the Heisenberg model with crystalline field. For the BEG model, systematic approximations of the exact partition function lead to the results of the Molecular Field theory and the non-renormalized high-density expansion theory. Having recourse to the variational principle, the thermodynamical properties of the Blume-Capel model as well as those of the quadrupolar Ising model with single-ion anisotropy are studied in detail. Similarly, for the Heisenberg model with crystalline field, results of the high-density expansion theory are obtained. The application of the Feynman variational principle is also analysed.