RT journal article
T1 Cluster density functional theory for lattice models based on the theory of Möbius functions
A1 Lafuente Molinero, Luis
A1 Cuesta, J.A.
A2 Matemáticas
AB 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.
PB Institute of Physics Publisihing
SN 0305-4470
YR 2005
FD 2005-08-10
LK http://hdl.handle.net/10498/30843
UL http://hdl.handle.net/10498/30843
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 09-may-2026