Lattice Fundamental Measure Theory beyond 0D Cavities: Dimers on Square Lattices

TL;DR

This paper extends a lattice fundamental measure theory functional for dimers on square lattices, improving accuracy in bulk and confined systems, especially at high densities, by ensuring exactness on small cavities.

Contribution

It derives an extended free energy functional that is exact on cavities holding up to two particles, enhancing previous models for lattice dimers.

Findings

Improved free energy predictions at high packing fractions.

Functional is exact for cavities with up to two particles.

Enhanced accuracy in both bulk and confined systems.

Abstract

Using classical density functional theory, we study the behavior of dimers, i.e. hard rods of length $L=2$, on a two-dimensional cubic lattice. For deriving a free energy functional, we employ Levy's prescription which is based on the minimization of a microscopic free energy with respect to the many-body probability under the constraint of a fixed density profile. Using that, we recover the functional originally found by Lafuente and Cuesta and derive an extension. With this extension, the free energy functional is exact on cavities that can hold at most two particles simultaneously. The new functional improves the prediction of the free energy in bulk as well as in highly confined systems, especially for high packing fractions, in comparison to that of Lafuente and Cuesta.