Finite Lattice and Phenomenological Approximations for the Anomaly in the Density of a Water-like Lattice Gas Model

TL;DR

This paper models a water-like lattice gas, solves it exactly on a finite lattice, and develops a phenomenological theory to describe its density anomaly, providing insights into phase behavior and density fluctuations.

Contribution

It introduces an exactly solvable two-dimensional lattice gas model with a phenomenological approach for density anomalies, linking microscopic interactions to macroscopic phase behavior.

Findings

Exact partition function obtained for the lattice model

Identification of a density anomaly region in the phase diagram

Phenomenological density theory aligns with simulation results

Abstract

We propose a model for a two dimensional, associative water-like lattice gas with one single variable representing both long and short-range interactions. The corresponding hamiltonian was solved exactly, by state enumeration in a finite lattice, so to obtain an analytic expression for the partition function. The lattice dimensions were chosen based on geometric characteristics of the stable phases found in previous works using Monte Carlo simulations. An expression for the particle density in the finite lattice was then obtained, and coexistence curves with a region of anomaly in the density presented in a phase diagram. In the end, a phenomenological theory for the system density is proposed and compared to the previous results.