Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2005-08-19
Phys. Rev. E 72, 061112 (2005)
Physics
Condensed Matter
Statistical Mechanics
Minor changes in accordance with referee comments
Scientific paper
10.1103/PhysRevE.72.061112
The Hierarchical Reference Theory (HRT) and the Self-Consistent Ornstein-Zernike Approximation (SCOZA) are two liquid state theories that both furnish a largely satisfactory description of the critical region as well as phase separation and the equation of state in general. Furthermore, there are a number of similarities that suggest the possibility of a unification of both theories. As a first step towards this goal we consider the problem of combining the lowest order gamma expansion result for the incorporation of a Fourier component of the interaction with the requirement of consistency between internal and free energies, leaving aside the compressibility relation. For simplicity we restrict ourselves to a simplified lattice gas that is expected to display the same qualitative behavior as more elaborate models. It turns out that the analytically tractable Mean Spherical Approximation is a solution to this problem, as are several of its generalizations. Analysis of the characteristic equations shows the potential for a practical scheme and yields necessary conditions any closure to the Ornstein Zernike relation must fulfill for the consistency problem to be well posed and to have a unique differentiable solution. These criteria are expected to remain valid for more general discrete and continuous systems, even if consistency with the compressibility route is also enforced where possible explicit solutions will require numerical evaluations.
Hoye Johan S.
Reiner Albert
No associations
LandOfFree
Towards a unification of HRT and SCOZA does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Towards a unification of HRT and SCOZA, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Towards a unification of HRT and SCOZA will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-365371