Breakdown of Multipole Expansion in Emergent Electromagnetism
Abstract
We find a striking departure from simple electrostatics in a family of two-dimensional lattice models whose effective description takes the form of an emergent electromagnetism: a high-order multipolar charge configuration can induce an electric field characteristic of a \textit{lower-}order multipole. Studying the archetypical hardcore dimer and U(1) spin-1/2 link models, we trace this to a breakdown of the superposition principle: for dense charge configurations, there can be a nonlinear suppression, or even enhancement, of the far field compared to the linear expectation. Our work establishes that microscopic lattice-scale constraints in models for emergent electromagnetism can change the far-field behaviour to differ from often utilized long-wavelength descriptions in standard effective continuum models.
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BibTeX
@misc{benami2026breakdown,
title = {{Breakdown of Multipole Expansion in Emergent Electromagnetism}},
author = {Tom Ben-Ami and Markus Heyl and Roderich Moessner},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12063},
eprint = {2609.12063},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12063},
}
RIS
TY - UNPB
TI - Breakdown of Multipole Expansion in Emergent Electromagnetism
AU - Tom Ben-Ami
AU - Markus Heyl
AU - Roderich Moessner
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.12063
UR - https://arxiv.org/abs/2609.12063
AB - We find a striking departure from simple electrostatics in a family of two-dimensional lattice models whose effective description takes the form of an emergent electromagnetism: a high-order multipolar charge configuration can induce an electric field characteristic of a \textit{lower-}order multipole. Studying the archetypical hardcore dimer and U(1) spin-1/2 link models, we trace this to a breakdown of the superposition principle: for dense charge configurations, there can be a nonlinear suppression, or even enhancement, of the far field compared to the linear expectation. Our work establishes that microscopic lattice-scale constraints in models for emergent electromagnetism can change the far-field behaviour to differ from often utilized long-wavelength descriptions in standard effective continuum models.
ER -