Is higher-order physics different?
Abstract
Group interactions are widespread, and higher-order extensions of familiar models display collective phenomena absent from their pairwise baselines, which are routinely offered as evidence of a distinct higher-order physics. We ask whether that claim survives the test that gives new a precise meaning in statistical physics: that of universality. Revisiting canonical higher-order models, we argue that what classifies collective behavior are the infrared ingredients that survive at long scales. Arity is not a universality label. Beyond universality, we examine two further questions: whether higher-order structure is a fact about the system or a choice of description, and what data can and cannot tell us about interaction order. Higher-order descriptions remain indispensable when they expose the organizing structure, provide a better mechanistic language, or improve prediction. We close with what should be measured before new phenomena can be claimed, and where higher-order structure already earns its place.
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BibTeX
@misc{villegas2026higherorder,
title = {{Is higher-order physics different?}},
author = {Pablo Villegas and Sandro Meloni},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20759},
eprint = {2609.20759},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20759},
}
RIS
TY - UNPB
TI - Is higher-order physics different?
AU - Pablo Villegas
AU - Sandro Meloni
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20759
UR - https://arxiv.org/abs/2609.20759
AB - Group interactions are widespread, and higher-order extensions of familiar models display collective phenomena absent from their pairwise baselines, which are routinely offered as evidence of a distinct higher-order physics. We ask whether that claim survives the test that gives new a precise meaning in statistical physics: that of universality. Revisiting canonical higher-order models, we argue that what classifies collective behavior are the infrared ingredients that survive at long scales. Arity is not a universality label. Beyond universality, we examine two further questions: whether higher-order structure is a fact about the system or a choice of description, and what data can and cannot tell us about interaction order. Higher-order descriptions remain indispensable when they expose the organizing structure, provide a better mechanistic language, or improve prediction. We close with what should be measured before new phenomena can be claimed, and where higher-order structure already earns its place.
ER -