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Calculation of the Helmholtz free energy with approximate Green's functions

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  • Figueira, M.S.
  • Foglio, M.E.

Abstract

We employ approximate Green's Functions (GF) to obtain the Helmholtz free energy F in a Grand Canonical Ensemble. This study was motivated by the calculation of the total number of electrons Nt as a function of the chemical potential μ in the Periodic Anderson Model by employing approximate one-electron GF. In this calculation we found that for some parameter values at low T one obtains three values of the chemical potential μ for each Nt in a small interval of Nt. One of the three states is thermodynamically unstable because Nt decreases when μ increases, but in the calculation of F by a methods that is based in a thermodynamic relation, this is the most stable of the three. The purpose of this work is to explain this paradox, and we also suggest a variation of the calculation that avoids this difficulty. From geometrical arguments it is clear that this paradox will be always present when Nt vs. μ has the shape observed in our calculation, independently of the numerical details of the calculation.

Suggested Citation

  • Figueira, M.S. & Foglio, M.E., 1994. "Calculation of the Helmholtz free energy with approximate Green's functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 208(2), pages 279-286.
    • Handle: RePEc:eee:phsmap:v:208:y:1994:i:2:p:279-286
    DOI: 10.1016/0378-4371(94)00043-3
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