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 N t 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 N t in a small interval of N t . One of the three states is thermodynamically unstable because N t 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 N t vs. μ has the shape observed in our calculation, independently of the numerical details of the calculation.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Physica A: Statistical Mechanics and its Applications
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.