Universal behavior at the Lifshitz Points of an active Malthusian Ising model

Abstract

Lifshitz points (LPs) are multicritical points where ordered, disordered, and patterned 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 entirely unexplored. Here we address this gap by introducing and analyzing LPs in the Active Malthusian Ising Model (AMIM) -- a minimal model of living matter that incorporates motility together with birth-death dynamics. Despite its simplicity, the AMIM provides direct experimental relevance. We show that the system generically exhibits two distinct LPs and elucidate their universal behavior using a dynamic renormalization group analysis with the $\epsilon$-expansion method at one loop. Our results yield testable predictions for future simulations and experiments, establishing LPs as a fertile testing ground for novel physics in active matter.