Critical scaling and supercritical coarsening in Active Model B+

TL;DR

This study investigates critical dynamics and phase-ordering in Active Model B+ using simulations, revealing mean-field scaling at criticality and logarithmic corrections in domain growth, with activity influencing microphase separation.

Contribution

It provides the first detailed analysis of critical and supercritical coarsening in Active Model B+ with new insights into growth laws and phase diagram construction.

Findings

Mean-field scaling with decay exponent α=1/4 at criticality

Logarithmic corrections to domain growth law in supercritical quenches

Active current suppresses macro-cluster formation in AMB+

Abstract

We study critical dynamics and phase-ordering kinetics in Active Model B (AMB) and its minimal extension, Active Model B$+$ (AMB$+$), using deterministic simulations in two dimensions. At criticality $r_c=0$, both models display identical mean-field scaling despite nonequilibrium currents, with order-parameter decay with time as $m(t)\sim t^{-\alpha}$, with $\alpha=\frac14$, and dynamical exponent being $z=4$. A generalized equal-area construction yields the binodal densities and phase diagram of AMB$+$. For supercritical quenches, domain size grows as $L(t)\sim t^{1/3}(1+c/\ln t)$, revealing logarithmic corrections to the classic $t^{1/3}$ growth-law; moreover it is consistent with the functional renormalization group predictions for marginal activity in $d=2$. While the logarithmic corrections are quite prominent in AMB, in AMB$+$ they are suppressed as the active current acts against the formation of macro-clusters; the growth is eventually arrested when a long-lived microphase-separated state appears.