A density functional for the lattice gas from fundamental measure theory

TL;DR

This paper develops a density functional for lattice gases using fundamental measure theory, accurately capturing phase behavior and interface tensions, and improving upon standard mean-field models.

Contribution

It introduces a novel density functional based on lattice fundamental measure theory for the lattice gas and Ising models, incorporating polymer clusters and depletion effects.

Findings

Recovers Bethe-Peierls approximation in bulk phase diagram

Planar interface tensions are closer to simulation results than standard models

Demonstrates interface solutions away from coexistence with constrained interface positions

Abstract

We construct a density functional for the lattice gas / Ising model on square and cubic lattices based on lattice fundamental measure theory. In order to treat the nearest-neighbor attractions between the lattice gas particles, the model is mapped to a multicomponent model of hard particles with additional lattice polymers where effective attractions between particles arise from the depletion effect. The lattice polymers are further treated via the introduction of polymer clusters (labelled by the numbers of polymer they contain) such that the model becomes a multicomponent model of particles and polymer clusters with nonadditive hard interactions. The density functional for this nonadditive hard model is constructed with lattice fundamental measure theory. The resulting bulk phase diagram recovers the Bethe-Peierls approximation and planar interface tensions show a considerable improvement compared to the standard mean-field functional and are close to simulation results in three dimensions. We demonstrate the existence of planar interface solutions at chemical potentials away from coexistence when the equimolar interface position is constrained to arbitrary real values.