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On exact solutions to three-dimensional Yukawa lattice model and BCC to FCC phase transitions
Abstract
We determine the global minimizers of the three-dimensional Yukawa lattice energy at every fixed density. At unit covolume, BCC is the unique minimizer below a transition parameter κ*≈1.7179218684699, FCC is the unique minimizer above it, and exactly these two lattice classes minimize at the transition. Mathematically, denote the Yukawa potential and the energy per particle under this potential by vκ(r)=(e−κr)/r, Eκ(L)=1/2∑v∈ L∖{0} (e−κ|v|)/|v|. Then, argmin|L|=1Eκ(L)= BCC lattice,&0<κ<κ*, BCC or FCC lattice,&κ=κ*, FCC lattice,&κ>κ*. As a consequence, the zero-screening comparison recovers the unique BCC minimum for the renormalized Coulomb energy.
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BibTeX
@misc{luo2026exact,
title = {{On exact solutions to three-dimensional Yukawa lattice model and BCC to FCC phase transitions}},
author = {Senping Luo and Juncheng Wei},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31456},
eprint = {2610.31456},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31456},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On exact solutions to three-dimensional Yukawa lattice model and BCC to FCC phase transitions
AU - Senping Luo
AU - Juncheng Wei
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31456
UR - https://arxiv.org/abs/2610.31456
AB - We determine the global minimizers of the three-dimensional Yukawa lattice energy at every fixed density. At unit covolume, BCC is the unique minimizer below a transition parameter κ_*≈1.7179218684699, FCC is the unique minimizer above it, and exactly these two lattice classes minimize at the transition. Mathematically, denote the Yukawa potential and the energy per particle under this potential by v_κ(r)=(e^−κr)/r, E_κ(L)=1/2∑_v∈ L∖{0} (e^−κ|v|)/|v|. Then, argmin_|L|=1E_κ(L)= BCC lattice,&0<κ<κ_*, BCC or FCC lattice,&κ=κ_*, FCC lattice,&κ>κ_*. As a consequence, the zero-screening comparison recovers the unique BCC minimum for the renormalized Coulomb energy.
ER -