Cluster density functional theory for lattice models based on the theory of Mobius functions

Details Cluster density functional theory for lattice models based on the theory of Mobius functions Cluster density functional theory for lattice models based on the theory of Mobius functions

2005-04-18

arxiv.org/abs/cond-mat/0504413v1

J. Phys. A: Math. Gen. 38, 7461-7482 (2005)

Physics

Condensed Matter

Statistical Mechanics

21 pages, 2 figures, uses iopart.cls, as well as diagrams.sty (included)

Scientific paper

10.1088/0305-4470/38/34/002

Rosenfeld's fundamental measure theory for lattice models is given a rigorous formulation in terms of the theory of Mobius functions of partially ordered sets. The free-energy density functional is expressed as an expansion in a finite set of lattice clusters. This set is endowed a partial order, so that the coefficients of the cluster expansion are connected to its Mobius function. Because of this, it is rigorously proven that a unique such expansion exists for any lattice model. The low-density analysis of the free-energy functional motivates a redefinition of the basic clusters (zero-dimensional cavities) which guarantees a correct zero-density limit of the pair and triplet direct correlation functions. This new definition extends Rosenfeld's theory to lattice model with any kind of short-range interaction (repulsive or attractive, hard or soft, one- or multi-component...). Finally, a proof is given that these functionals have a consistent dimensional reduction, i.e. the functional for dimension d' can be obtained from that for dimension d (d'

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