Two-dimensional structures formed by pair potentials: An analytical and numerical study
Abstract
Understanding the thickness dependence of the excess energy of thin films and identifying the deviation from the scaling law that holds for thicker films are crucial for predicting the formation of two-dimensional (2D) materials derived from nonlayered structures, commonly referred to as non-van der Waals (non-vdW) 2D materials. Here, we analytically study the excess energy of thin films as a function of the number of layers N, assuming pair potentials. We show that the 1/N scaling law of the excess energy breaks down in the monolayer limit when the interatomic interactions are long-ranged. The analytical results are confirmed by numerical simulations using the Lennard-Jones and Morse potentials. The present work suggests that non-vdW 2D structures can be formed by pair potentials alone.
Related
- Mass-Scaling of Quantum Tunnelling in Hydrogen Bonds: Analytical Model and Comparison with Multidimensional Potentials
- Numerical speckle reduction for optical coherence tomography based on an analytical image formation model
- Generalizable Equivariant Diffusion Models for Non-Abelian Lattice Gauge Theory: Analytical Foundations and Numerical Scaling Tests
- The Scalar MSW Effect: Compact analytical formulas for neutrino oscillations with large matter effects, including μ−μ and τ−τ dominant matter potentials
- Breaking Behavioral Uniformity in Traffic Flow: Analytical Derivation and Numerical Verification of Optimal Cooperative Buffering
BibTeX
@misc{ono2026twodimensional,
title = {{Two-dimensional structures formed by pair potentials: An analytical and numerical study}},
author = {Shota Ono},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29421},
eprint = {2610.29421},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29421},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Two-dimensional structures formed by pair potentials: An analytical and numerical study
AU - Shota Ono
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29421
UR - https://arxiv.org/abs/2610.29421
AB - Understanding the thickness dependence of the excess energy of thin films and identifying the deviation from the scaling law that holds for thicker films are crucial for predicting the formation of two-dimensional (2D) materials derived from nonlayered structures, commonly referred to as non-van der Waals (non-vdW) 2D materials. Here, we analytically study the excess energy of thin films as a function of the number of layers N, assuming pair potentials. We show that the 1/N scaling law of the excess energy breaks down in the monolayer limit when the interatomic interactions are long-ranged. The analytical results are confirmed by numerical simulations using the Lennard-Jones and Morse potentials. The present work suggests that non-vdW 2D structures can be formed by pair potentials alone.
ER -