# Complete catalog of ground-state diagrams for the general three-state lattice-gas model with nearest-neighbor interactions on a square lattice

## TL;DR

This paper provides a comprehensive classification of all possible ground-state phase diagrams for a three-state lattice-gas model with nearest-neighbor interactions on a square lattice, covering the full five-dimensional parameter space.

## Contribution

It presents the complete catalog of fifteen topologically different ground-state diagrams, extending previous work that identified only six.

## Key findings

- Fifteen distinct ground-state diagrams identified
- Complete parameter space exploration conducted
- Results applicable to lattice-gas and Ising-spin models

## Abstract

The ground states of the general three-state lattice-gas (equivalently, $S=1$ Ising) model with nearest-neighbor interactions on a square lattice are explored in the full, five-dimensional parameter space of three interaction constants and two generalized chemical potentials or fields. The resulting, complete catalog of fifteen topologically different ground-state diagrams (zero-temperature phase diagrams) is discussed in both lattice-gas and Ising-spin language. The results extend those of a recent study in a reduced parameter space [V. F. Fefelov, et al., Phys. Chem. Chem. Phys., 2018, 20, 10359--10368], which identified six different ground-state diagrams.