The Ising lattice gas and the surface diffusion of CO on Cu(001) at finite coverage
Abstract
The memory equation of the coherent intermediate scattering function (ISF), derived previously for lattice gases, is applied to the Ising lattice gas under Kawasaki dynamics. The ISF follows the decay of a density wave of adparticles, a superposition of exponential relaxation modes: the decay starts at a rate fixed by a sum rule and is then slowed by a memory. The static structure factor and the effective hop rate are obtained in closed form, exactly along a one-dimensional channel; with the sum rule they give a single exponential, a lower bound on the ISF. Exact relaxation spectra show that this single exponential, built from equilibrium quantities alone, reproduces the correlation time only at weak coupling; only there can a measured dephasing rate be read through the statics. For strong attraction the slow dissolution of clusters lengthens the correlation time up to ninefold, whereas a repulsive layer relaxes nearly as a single mode at its structure peak. The dephasing rate, fitted over a time window where it is nearly constant, approaches the slowest relaxation rate, not the initial one; the sum rule reaches the data only through the area beneath the normalized decay, which defines the correlation time. For CO/Cu(001), the lattice gas reproduces the dephasing rates measured along two crystal directions and requires a nearest-neighbour repulsion of at least $35−−50$~meV, whatever the jump rates; the measured rate is then close to the inverse correlation time, and the memory is predicted to grow with coverage.
Related
- Surface diffusion with lateral interactions: a closed-form intermediate scattering function of an Ising adlayer from the memory-equation formalism
- Anisotropic ising model on 2D Kagomé lattice as an inhomogeneous XYZ integrable model
- The free energy of the square lattice Ising model with interactions alternating in horizontal and vertical directions
- Anizotropic Ising Model on 2D Kagomé Lattice as an Inhomogeneous XYZ Integrable Model
- Local-dynamics accessibility of the stripe phase in the triangular-lattice J1-J2 Ising antiferromagnet
BibTeX
@misc{miretartes2026ising,
title = {{The Ising lattice gas and the surface diffusion of CO on Cu(001) at finite coverage}},
author = {S. Miret-Artés},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33147},
eprint = {2610.33147},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33147},
}
RIS
TY - UNPB
TI - The Ising lattice gas and the surface diffusion of CO on Cu(001) at finite coverage
AU - S. Miret-Artés
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.33147
UR - https://arxiv.org/abs/2610.33147
AB - The memory equation of the coherent intermediate scattering function (ISF), derived previously for lattice gases, is applied to the Ising lattice gas under Kawasaki dynamics. The ISF follows the decay of a density wave of adparticles, a superposition of exponential relaxation modes: the decay starts at a rate fixed by a sum rule and is then slowed by a memory. The static structure factor and the effective hop rate are obtained in closed form, exactly along a one-dimensional channel; with the sum rule they give a single exponential, a lower bound on the ISF. Exact relaxation spectra show that this single exponential, built from equilibrium quantities alone, reproduces the correlation time only at weak coupling; only there can a measured dephasing rate be read through the statics. For strong attraction the slow dissolution of clusters lengthens the correlation time up to ninefold, whereas a repulsive layer relaxes nearly as a single mode at its structure peak. The dephasing rate, fitted over a time window where it is nearly constant, approaches the slowest relaxation rate, not the initial one; the sum rule reaches the data only through the area beneath the normalized decay, which defines the correlation time. For CO/Cu(001), the lattice gas reproduces the dephasing rates measured along two crystal directions and requires a nearest-neighbour repulsion of at least $35−−50$~meV, whatever the jump rates; the measured rate is then close to the inverse correlation time, and the memory is predicted to grow with coverage.
ER -