We formulate the spectral-density method in classical statistical mechanics in strict analogy with the known quantum version, and we apply it to the classical Heisenberg ferromagnetic model in an external field. A new formula for the magnetization in the classical formulation of spin-vector Green functions is derived for arbitrary spatial dimensionality. Furthermore, the static properties of the oneand three-dimensional cases are considered in detail. We obtain accurate results over a wide range of temperatures with the external field for the one-dimensional model and without field for the three-dimensional model. In the first case very good agreement with the exact numerical transfer-matrix data is also found in the region of higher temperature where the interacting-boson approach fails. In particular the zero-field susceptibility results are found to be consistent with the exact results obtained by Fisher.

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A study of the d-dimensional classical Heisenberg ferromagnetic model in the presence of a magnetic field is performed within the two-time Green function's framework in classical statistical physics. We extend the well known quantum Callen method to derive analytically a new formula for magnetization. Although this formula is valid for any dimensionality, we focus on one- and three- dimensional models and compare the predictions with those arising from a different expression suggested many years ago in the context of the classical spectral density method. Both frameworks give results in good agreement with the exact numerical transfer-matrix data for the one-dimensional case and with the exact high-temperature-series results for the three-dimensional one. In particular, for the ferromagnetic chain, the zero-field susceptibility results are found to be consistent with the exact analytical ones obtained by M.E. Fisher. However, the formula derived in the present paper provides more accurate predictions in a wide range of temperatures of experimental and numerical interest.Comment: 19 pages, 3 figure

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The zero-field parallel and perpendicular susceptibility and the zero-field specific heat of the quantum easy-plane S=1 Heisenberg spin chains are calculated numerically and applied to TMNB, TMNC and CsNiF3. New values of the model parameters are estimated from fitting procedures. As to CsNiF3, the in-plane specific heat, the field-dependent magnetization and the spin-wave dispersion are also evaluated for a given choice of the microscopic parameters (J/kB=20.5 K, A/J=0.425) and compared with measured quantities. An overall agreement with experiment is revealed.