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Callen-like method for the classical Heisenberg ferromagnet

Author

Listed:
  • Campana, L.S.
  • Cavallo, A.
  • De Cesare, L.
  • Esposito, U.
  • Naddeo, A.

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.

Suggested Citation

  • Campana, L.S. & Cavallo, A. & De Cesare, L. & Esposito, U. & Naddeo, A., 2012. "Callen-like method for the classical Heisenberg ferromagnet," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1087-1096.
  • Handle: RePEc:eee:phsmap:v:391:y:2012:i:4:p:1087-1096
    DOI: 10.1016/j.physa.2011.10.007
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