# Doniach Lattice Gas on Bipartite Lattices in the Mean-Field Approximation

## TL;DR

This paper studies a statistical model for supramolecular structures using a mean-field approach, revealing new phase behaviors on bipartite lattices.

## Contribution

The study introduces an analysis of staggered phases in the Doniach lattice gas model on bipartite lattices using mean-field approximation.

## Key findings

- Staggered phases were identified in the Doniach lattice gas model on bipartite lattices.
- Intermediate topologies in phase diagrams were observed as parameters of the effective Hamiltonian changed.
- Theoretical results were compared with experimental data for DMPC using parameter fitting.

## Abstract

The Doniach lattice
gas (DLG) consists of a statistical model that
can be mapped into a spin-1 Ising model with highly degenerate single-site
states and the inclusionusing the nomenclature of the analogous
magnetic modelof dipole–quadrupole interactions, besides
the usual dipole–dipole, Zeeman-effect and crystal–field
interactions. Its formulation was motivated aiming at the study of
phase transitions in supramolecular structures of zwitterionic phospholipids,
in particular, allowing an alternative description of density fluctuations
in the system, already included in a certain class of lattice models
(Nagle, J. F. J. Chem. Phys.
1973, 58, 252; Nagle, J. F. J. Chem. Phys.
1975, 63, 1255), but not considered in previous
proposals of Ising-type models (Doniach, S. J. Chem. Phys.
1978, 68, 4912). In this work, we
investigate the DLG model, considering the division of the system
into two interpenetrating sublattices, under the framework of the
mean-field approximation. This analysis of the model on bipartite
lattices allowed the investigation of staggered phases, which were
overlooked in the first analysis of the model in the mean-field approach
(Guidi, H. S.; Henriques, V. B. Phys. Rev. E
2014, 90, 052705), precisely because it was
only assumed the presence of uniform phases, i.e., without splitting
the system into two distinct sublattices. However, such staggered
phases were observed for this model in the pair approximation on bipartite
lattices (de Oliveira, F. O.; Tamashiro, M. N. Phys. Rev.
E
2019, 99, 012147; de Oliveira,
F. O.; Tamashiro, M. N. Langmuir
2019, 35, 3848). Throughout the work, in addition to
the staggered phase, we also observed intermediate topologies of representative
phase diagrams (μ̅/z, t/z), which explain the development of the main topologies
as we change the parameters (
l̅
, k̅) associated
with the effective Hamiltonian interactions. Finally, we perform a
parameter fitting between theoretical results and isothermal compression
experimental data for the phospholipid 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC), allowing also a comparison between
the fittings obtained using the mean-field and the pair approximations.