Phase behavior of hard-core lattice gases: A Fundamental Measure approach

TL;DR

This paper applies an extended fundamental measure theory to lattice hard-core fluids, revealing complex phase diagrams and entropy-driven phase transitions in 2D and 3D lattice systems, including ordered and demixed phases.

Contribution

It introduces a novel application of fundamental measure theory to lattice hard-core fluids, enabling detailed mapping of phase diagrams including ordered phases.

Findings

Complete phase diagram for 2D parallel hard squares showing degenerated close packing.

Identification of multiple entropy-driven phase transitions in 3D binary hard cube mixture.

Discovery of various ordered and demixed phases through free energy minimization.

Abstract

We use an extension of fundamental measure theory to lattice hard-core fluids to study the phase diagram of two different systems. First, two-dimensional parallel hard squares with edge-length $\sigma=2$ in a simple square lattice. This system is equivalent to the lattice gas with first and second neighbor exclusion in the same lattice, and has the peculiarity that its close packing is degenerated (the system orders in sliding columns). A comparison with other theories is discussed. Second, a three-dimensional binary mixture of parallel hard cubes with $\sigma_{\rm{L}}=6$ and $\sigma_{\rm{S}}=2$. Previous simulations of this model only focused on fluid phases. Thanks to the simplicity introduced by the discrete nature of the lattice we have been able to map out the complete phase diagram (both uniform and nonuniform phases) through a free minimization of the free energy functional, so the structure of the ordered phases is obtained as a result. A zoo of entropy-driven phase transitions is found: one-, two- and three-dimensional positional ordering, as well as fluid-ordered phase and solid-solid demixings.