Universality class for a nonequilibrium state of matter: A d = 4 − ε expansion study of Malthusian flocks

Abstract

We show that “Malthusian flocks” – i.e., coherently moving collections of self-propelled entities(such as living creatures) which are being “born” and “dying” during their motion – belong toa new universality class in spatial dimensionsd >2. We calculate the universal exponents andscaling laws of this new universality class toO( ) in ad= 4− expansion, and find these aredifferent from the “canonical” exponents previously conjectured to hold for “immortal” flocks (i.e.,those without birth and death) and shown to hold for incompressible flocks with spatial dimensionsin the range of 2< d≤4. We also obtain a universal amplitude ratio relating the damping oftransverse and longitudinal velocity and density fluctuations in these systems. Furthermore, wefind a universal separatrix in real (r) space between two regions in which the equal time densitycorrelation〈δρ(r,t)δρ(0,t)〉has opposite signs. Our expansion should be quite accurate ind= 3,allowing precise quantitative comparisons between our theory, simulations, and experiments.