Disordered hyperuniform modulated phases and the cosmic web from one free energy
Abstract
Disordered hyperuniformity spans twenty-five orders of magnitude, from the microscopic world of soft and condensed matter to the distribution of matter in the universe. We introduce a free-energy functional with no adjustable coupling, a phase-field-crystal ordering term and a Newtonian tail, and show that its two kinetic limits generate two of these structures. Under conserved overdamped dynamics it arrests in a bicontinuous labyrinth of the kind found in confined fluids, block copolymers, active matter and vegetation patterns, which is a class III disordered hyperuniform state; under inertial dynamics in an expanding background it generates a cosmic web whose tidal skeleton matches that of gravity alone to within $0.03$ in every morphological class. In both limits the suppressed long-wavelength fluctuations are inherited from the initial condition rather than made by the dynamics: the large-scale exponent of the arrested state equals the primordial one, and gravity rescales the infrared spectrum by the linear growth factor to better than one per cent over a factor $1363$ of growth. The two sectors are continuously connected, and their distance is measurable: once the ordering modulation saturates, its mean-field back-reaction leaves the medium with a residual pressure proportional to λ02 that suppresses the growth of the largest scales by a smooth factor and vanishes in the cold-matter limit λ0→0.
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BibTeX
@misc{martelli2026disordered,
title = {{Disordered hyperuniform modulated phases and the cosmic web from one free energy}},
author = {Fausto Martelli},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11988},
eprint = {2609.11988},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11988},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Disordered hyperuniform modulated phases and the cosmic web from one free energy
AU - Fausto Martelli
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.11988
UR - https://arxiv.org/abs/2609.11988
AB - Disordered hyperuniformity spans twenty-five orders of magnitude, from the microscopic world of soft and condensed matter to the distribution of matter in the universe. We introduce a free-energy functional with no adjustable coupling, a phase-field-crystal ordering term and a Newtonian tail, and show that its two kinetic limits generate two of these structures. Under conserved overdamped dynamics it arrests in a bicontinuous labyrinth of the kind found in confined fluids, block copolymers, active matter and vegetation patterns, which is a class III disordered hyperuniform state; under inertial dynamics in an expanding background it generates a cosmic web whose tidal skeleton matches that of gravity alone to within $0.03$ in every morphological class. In both limits the suppressed long-wavelength fluctuations are inherited from the initial condition rather than made by the dynamics: the large-scale exponent of the arrested state equals the primordial one, and gravity rescales the infrared spectrum by the linear growth factor to better than one per cent over a factor $1363$ of growth. The two sectors are continuously connected, and their distance is measurable: once the ordering modulation saturates, its mean-field back-reaction leaves the medium with a residual pressure proportional to λ_0^2 that suppresses the growth of the largest scales by a smooth factor and vanishes in the cold-matter limit λ_0→0.
ER -