@misc{10498/30843,
year = {2005},
month = {8},
url = {http://hdl.handle.net/10498/30843},
abstract = {Rosenfeld's fundamental-measure theory for lattice models is given a rigorous formulation in terms of the theory of Möbius 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 with a partial order, so that the coefficients of the cluster expansion are connected to its Möbius 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 models with any kind of short-range interaction (repulsive or attractive, hard or soft, one or multicomponent ...). 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′ < d) if the latter is evaluated at a density profile confined to a d′-dimensional subset.},
publisher = {Institute of Physics Publisihing},
title = {Cluster density functional theory for lattice models based on the theory of Möbius functions},
doi = {10.1088/0305-4470/38/34/002},
author = {Lafuente Molinero, Luis and Cuesta, J.A.},
}