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Critical scaling and supercritical coarsening in active model B+

Abir Bhowmick1,* and P. K. Mohanty1,2,†

  • *Contact author: ab23rs019@iiserkol.ac.in
  • †Contact author: pkmohanty@iiserkol.ac.in
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Phys. Rev. E 114, 024134 – Published 17 August, 2026

DOI: https://doi.org/10.1103/qktx-n35r

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 rc=0, both models display identical mean-field scaling despite nonequilibrium currents, with order-parameter decay with time as m(t)∼t−α, with α=14, 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)∼t1/3(1+c/lnt), revealing logarithmic corrections to the classic t1/3 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.

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Phys. Rev. E 114, 024134– Published 17 August, 2026
  • Received 10 April 2026
  • Accepted 27 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by Max Planck Society.

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