A density functional theory for general hard-core lattice gases

TL;DR

This paper introduces a universal method to derive approximate free energy functionals for any hard-core lattice gas, ensuring consistency and ease of extension to models with attractions.

Contribution

It presents a simple, general procedure to construct fundamental measure functionals for diverse lattice gases, unifying previous results and enabling extensions to attractive interactions.

Findings

Provides a universal method applicable to any lattice gas

Ensures functionals are consistent via dimensional reduction

Facilitates extensions to attractive lattice models

Abstract

We put forward a general procedure to obtain an approximate free energy density functional for any hard-core lattice gas, regardless of the shape of the particles, the underlying lattice or the dimension of the system. The procedure is conceptually very simple and recovers effortlessly previous results for some particular systems. Also, the obtained density functionals belong to the class of fundamental measure functionals and, therefore, are always consistent through dimensional reduction. We discuss possible extensions of this method to account for attractive lattice models.