Critical scaling and supercritical coarsening in Active Model B+
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arXiv
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| Natura: | Preprint |
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2026
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| author | Bhowmick, Abir Mohanty, P. K. |
| author_facet | Bhowmick, Abir Mohanty, P. K. |
| contents | 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 $m(t)\sim t^{-α}$, with $α=\frac14$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07247 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Critical scaling and supercritical coarsening in Active Model B+ Bhowmick, Abir Mohanty, P. K. Statistical Mechanics Soft Condensed Matter 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 $m(t)\sim t^{-α}$, with $α=\frac14$, 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. |
| title | Critical scaling and supercritical coarsening in Active Model B+ |
| topic | Statistical Mechanics Soft Condensed Matter |
| url | https://arxiv.org/abs/2604.07247 |