The fluid-lattice gas isomorphism with application to liquid-vapor equilibrium in physisorbed monolayers
Abstract
Liquid-gas equilibrium is described using a pair of Ising-like thermodynamic variables. The first is a combination of density and energy fields that is even under phase coexistence, derived from the Gibbs-Duhem and Clausius-Clapeyron relations. The second is the normalized density deviation M=ρ/ρd−1, which distinguishes the coexisting phases and serves as an odd ordering variable. Combining these variables with the empirical linearities of the binodal diameter and the Zeno line leads to a projective mapping between continuum-fluid and lattice-gas states. The implications of such mapping are tested against coexistence-density and saturation pressure data for the two-dimensional Lennard-Jones fluid, as well as physisorbed molecular monolayers of simple molecular fluids like argon and methane. Finally, a heuristic microscopic interaction-variable formulation that motivates continuous fluids versus lattice model description is also discussed.
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BibTeX
@misc{shevchenko2026fluidlattice,
title = {{The fluid-lattice gas isomorphism with application to liquid-vapor equilibrium in physisorbed monolayers}},
author = {Lev Shevchenko and Volodymyr Kulinskii},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.08178},
eprint = {2606.08178},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.08178},
}
RIS
TY - UNPB
TI - The fluid-lattice gas isomorphism with application to liquid-vapor equilibrium in physisorbed monolayers
AU - Lev Shevchenko
AU - Volodymyr Kulinskii
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2606.08178
UR - https://arxiv.org/abs/2606.08178
AB - Liquid-gas equilibrium is described using a pair of Ising-like thermodynamic variables. The first is a combination of density and energy fields that is even under phase coexistence, derived from the Gibbs-Duhem and Clausius-Clapeyron relations. The second is the normalized density deviation M=ρ/ρ_d−1, which distinguishes the coexisting phases and serves as an odd ordering variable. Combining these variables with the empirical linearities of the binodal diameter and the Zeno line leads to a projective mapping between continuum-fluid and lattice-gas states. The implications of such mapping are tested against coexistence-density and saturation pressure data for the two-dimensional Lennard-Jones fluid, as well as physisorbed molecular monolayers of simple molecular fluids like argon and methane. Finally, a heuristic microscopic interaction-variable formulation that motivates continuous fluids versus lattice model description is also discussed.
ER -