Solution of an associating lattice gas model with density anomaly on a Husimi lattice

TL;DR

This paper presents an exact solution of a simplified lattice gas model with orientational bonding on a Husimi lattice, revealing phase behavior and density anomalies consistent with simulations but differing from previous theoretical predictions.

Contribution

It provides the first exact solution of a hydrogen-bonding lattice gas model with density anomalies on a Husimi lattice, clarifying phase transitions and density behavior.

Findings

Identifies three phases: gas, HDL, and LDL, with all transitions discontinuous.

Finds lines of maximum and minimum densities in different phases.

Results align quantitatively with simulations but differ from earlier theoretical models.

Abstract

We study a model of a lattice gas with orientational degrees of freedom which resemble the formation of hydrogen bonds between the molecules. In this model, which is the simplified version of the Henriques-Barbosa model, no distinction is made between donors and acceptors in the bonding arms. We solve the model in the grand-canonical ensemble on a Husimi lattice built with hexagonal plaquettes with a central site. The ground-state of the model, which was originally defined on the triangular lattice, is exactly reproduced by the solution on this Husimi lattice. In the phase diagram, one gas and two liquid (high density-HDL and low density-LDL) phases are present. All phase transitions (GAS-LDL, GAS-HDL, and LDL-HDL) are discontinuous, and the three phases coexist at a triple point. A line of temperatures of maximum density (TMD) in the isobars is found in the metastable GAS phase, as well as another line of temperatures of minimum density (TmD) appears in the LDL phase, part of it in the stable region and another in the metastable region of this phase. These findings are at variance with simulational results for the same model on the triangular lattice, which suggested a phase diagram with two critical points. However, our results show very good quantitative agreement with the simulations, both for the coexistence loci and the densities of particles and of hydrogen bonds. We discuss the comparison of the simulations with our results.