STABILITY OF THE THERMAL HARTREE-FOCK APPROXIMATION
The thermal Hartree-Fock approximation of Green's function theory is shown to be equivalent, in its thermodynamic consequences, to the use of that density matrix that makes the free energy stationary over a simply restricted class of trial density matrices. The variational formulation provides a stability condition requiring one to reject those solutions of the thermal Hartree-Fock equations that do not correspond to local minima of the free energy. If only stable Hartree-Fock propagators are used, then the spectrum of density oscillations as calculated in the thermal random phase approximation can be shown to have only real frequencies. Reasons for the thermal RPA becoming unstable may therefore be found from studying the significance of unstable Hartree-Fock solutions. It is shown that isothermals with positive siope can occur in the Hartree-Fock equation of state only if an unstable solution has been used. This suggests that one type of instability is associated with a flrst order phase transition. This is confirmed when the approximation is applied to a lattice gas with attractive interactions. The equation of state is of the van der Waals type if the stability condition is ignored. If only solutions that give global minima to the free energy are used, the corrected isothermals are those that result from applying the Maxwell equal area construction to the naive ones. Unstable solutions correspond to the parts of the van der Waals isothermals with positive slope. The physically metastable parts correspond to solutions that are local but not global minima. A lattice gas with repulsive interactions illustrates another type of instability, characterizing a second order phase transition. In this case the naive solution becomes unstable even though no pathological behavior appears in its equation of state, and solutions corresponding to a spatially nonuniform density of particles are required to restore stability. (auth)
- Research Organization:
- Univ. of Birmingham, Eng.
- NSA Number:
- NSA-17-024280
- OSTI ID:
- 4684458
- Journal Information:
- Annals of Physics (New York) (U.S.), Journal Name: Annals of Physics (New York) (U.S.) Vol. Vol: 21; ISSN APNYA
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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