Critical scaling and supercritical coarsening in active model B

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)∼t^{-α}, with α=1/4, and the 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)∼t^{1/3}(1+c/lnt), 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. The logarithmic corrections are clearly evident in both AMB and AMB+ in the macrophase-separated regime. However, in AMB+, domain growth is arrested in the parameter regime where the active current opposes the formation of macroscopic clusters, leading to long-lived microphase-separated states.