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We consider a dynamical field theory (Active Model B+) that minimally extendsthe equilibrium Model B for diffusive phase separation of a scalar field, byadding leading-order terms that break time-reversal symmetry. It was recentlyshown that such active terms can cause the bulk phase separation of Model B tobe replaced by a steady state of microphase separation at a finite lengthscale. This phenomenon was understood at mean-field level as due to theactivity-induced reversal of the Ostwald ripening mechanism, which provides thekinetic pathway to bulk phase separation in passive fluids. This reversaloccurs only in certain ranges for the activity parameters. In this paper we gobeyond such a mean-field analysis and develop a $1$-loop Renormalisation Group(RG) approach. We first show that, in the parameter range where bulk phaseseparation is still present, the critical point belongs formally to the same(Wilson-Fisher) universality class as the passive Model B. In contrast, in aparameter range associated with microphase separation, we find that an unstablenon-equilibrium fixed point of the RG flow arises for $d\geq 2$, colliding withthe Wilson-Fisher point in $d\to 2^+$ and making it unstable in $d=2$. At largeactivity, the flow in this region is towards strong coupling. We argue that thephase transition to microphase separation in active systems, in the physicallyrelevant dimensions $d=2$ and $3$, very probably belongs to a newnon-equilibrium universality class. Because it is governed by thestrong-coupling regime of the RG flow, our perturbative analysis leaves openthe quantitative characterization of this new class.

From bulk to microphase separation in scalar active matter: A perturbative renormalization group analysis