Density functional theory for nearest-neighbor exclusion lattice gasses in two and three dimensions

Abstract

To speak about fundamental measure theory obliges to mention dimensional crossover. This feature, inherent to the systems themselves, was incorporated in the theory almost from the beginning. Although at first it was thought to be a consistency check for the theory, it rapidly became its fundamental pillar, thus becoming the only density functional theory which possesses such a property. It is straightforward that dimensional crossover connects, for instance, the parallel hard cube system (three-dimensional) with that of squares (two-dimensional) and rods (one-dimensional). We show here that there are many more connections which can be established in this way. Through them we deduce from the functional for parallel hard (hyper)cubes in the simple (hyper)cubic lattice the corresponding functionals for the nearest-neighbor exclusion lattice gases in the square, triangular, simple cubic, face-centered cubic, and body-centered cubic lattices. As an application, the bulk phase diagram for all these systems is obtained.

arXiv comment13 pages, 13 figures; needs revtex4

References in corpus (7)

• Capillary condensation in disordered porous materials: hysteresis versus equilibrium behavior
• Dimensional crossover of the fundamental-measure functional for parallel hard cubes
• Fundamental measure theory for lattice fluids with hard core interactions
• Phase behavior of hard-core lattice gases: A Fundamental Measure approach
• Demixing of colloid-polymer mixtures in poor solvents
• Absence of re-entrant phase transition of the antiferromagnetic Ising model on the simple cubic lattice: Monte Carlo study of the hard-sphere lattice gas
• Universality in the Three-Dimensional Hard-Sphere Lattice Gas

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• Multiple Phase Transitions in Extended Hard Core Lattice Gas Models in Two Dimensions
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• Phase diagram of a two-dimensional lattice gas model of a ramp system
• Lattice Model of an Ionic Liquid at an Electrified Interface
• The High Density Phase of the $k$-NN Hard Core Lattice Gas Model
• Phase transitions in a system of hard $Y$-shaped particles on the triangular lattice
• Liquid-Hextic-Solid Phase Transition of a Hard-Core Lattice Gas with Third Neighbor Exclusion
• Cluster density functional theory for lattice models based on the theory of Mobius functions
• Exact density functional for hard rod mixtures derived from Markov chain approach
• Husimi lattice solutions and the coherent-anomaly-method analysis for hard-square lattice gases
• Fundamental-measure density functional for the fluid of aligned hard hexagons: New insights in fundamental measure theory
• Lattice density functional for colloid-polymer mixtures: Multi-occupancy versus Highlander version
• Interacting hard rods on a lattice: Distribution of microstates and density functionals