Callen-like method for the classical Heisenberg ferromagnet

L.S. Campana, A. Cavallo, L. De Cesare, U. Esposito and A. Naddeo

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 4, 1087-1096

Abstract: 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.

Keywords: Classical statistical mechanics; Magnetism; Green functions (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:4:p:1087-1096

DOI: 10.1016/j.physa.2011.10.007

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