Interacting hard rods on a lattice: Distribution of microstates and density functionals

Abstract

We derive exact density functionals for systems of hard rods with first-neighbor interactions of arbitrary shape but limited range on a one-dimensional lattice. The size of all rods is the same integer unit of the lattice constant. The derivation, constructed from conditional probabilities in a Markov chain approach, yields the exact joint probability distribution for the positions of the rods as a functional of their density profile. For contact interaction ("sticky core model") between rods we give a lattice fundamental measure form of the density functional and present explicit results for contact correlators, entropy, free energy, and chemical potential. Our treatment includes inhomogeneous couplings and external potentials.

8 pages, 5 figures

References in corpus (7)

• A density functional theory for general hard-core lattice gases
• Penetrable Square-Well fluids: Exact results in one dimension
• Multicomponent adhesive hard sphere models and short-ranged attractive interactions in colloidal or micellar solutions
• Capillary ordering and layering transitions in two-dimensional hard-rod fluids
• Jammed disks in narrow channel: criticality and ordering tendencies
• Biaxial nematic and smectic phases of parallel particles with different cross sections
• Surface and smectic layering transitions in binary mixtures of parallel hard rods

Cited by in corpus (6)

• Statistically interacting vacancy particles
• Density profiles of a self-gravitating lattice gas in one, two, and three dimensions
• Monodisperse hard rods in external potentials
• Interacting hard-sphere fluids in an external field
• D-dimensional self-gravitating lattice gas in general relativity
• Thermodynamics of interacting hard rods on a lattice