Universal behavior at the Lifshitz points of an active Malthusian Ising model
File(s)
Accepted version
Author(s)
Legrand, Gabriel
Lee, Chiu Fan
Type
Journal Article
Abstract
Lifshitz points (LPs) are multicritical points where ordered, disordered, and modulated phases meet. Originally studied in equilibrium magnetic systems, LPs have since been identified in soft matter and even cosmological settings. Their role in active, living matter, however, remains
unexplored. Here we address this gap by introducing and analysing LPs in the Active Malthusian Ising Model (AMIM), aminimal modelofliving matter that combines active motility with birth–death dynamics. Weshowthatthisnonequilibrium system generically admits two distinct LPs: longitudinal
and transverse, and characterise their universal behaviour using a dynamical renormalisation group (RG)analysis basedonaone-loopϵ-expansion. At the longitudinal LP, the active nonlinearity drives a runaway RG flow, suggesting either a fluctuation-induced discontinuous transition or
the emergence of a strong-coupling fixed point beyond perturbation theory. In contrast, the transverse LP generically flows to the equilibrium anisotropic Lifshitz universality class (UC). Remarkably, upon further fine-tuning a nonlinear coupling, a new nonequilibrium UC emerges
whose scaling exponents can be determined exactly due to an emergent Galilean invariance. Our results provide concrete predictions for simulations and experiments, establishing Lifshitz multicriticality as a fertile testing ground for new universal behaviour in active matter.
unexplored. Here we address this gap by introducing and analysing LPs in the Active Malthusian Ising Model (AMIM), aminimal modelofliving matter that combines active motility with birth–death dynamics. Weshowthatthisnonequilibrium system generically admits two distinct LPs: longitudinal
and transverse, and characterise their universal behaviour using a dynamical renormalisation group (RG)analysis basedonaone-loopϵ-expansion. At the longitudinal LP, the active nonlinearity drives a runaway RG flow, suggesting either a fluctuation-induced discontinuous transition or
the emergence of a strong-coupling fixed point beyond perturbation theory. In contrast, the transverse LP generically flows to the equilibrium anisotropic Lifshitz universality class (UC). Remarkably, upon further fine-tuning a nonlinear coupling, a new nonequilibrium UC emerges
whose scaling exponents can be determined exactly due to an emergent Galilean invariance. Our results provide concrete predictions for simulations and experiments, establishing Lifshitz multicriticality as a fertile testing ground for new universal behaviour in active matter.
Date Acceptance
2026-05-21
Citation
Newton
ISSN
2950-6360
Publisher
Cell Press
Journal / Book Title
Newton
Copyright Statement
Copyright This paper is embargoed until publication. Once published the author’s accepted manuscript will be made available under a CC-BY License in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy).
License URL
Publication Status
Accepted