Spectral origin of conformal invariance in active nematic turbulence
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915943195607040 |
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| author | Redrouthu, Rithvik |
| author_facet | Redrouthu, Rithvik |
| contents | Zero-vorticity contours in the collective flows of living cells obey Schramm-Loewner evolution with diffusivity $κ= 6$ and thus fall in the universality class of critical percolation. This observation is surprising because the underlying vorticity field has long-range correlations that, according to the Weinrib-Halperin criterion, should alter the universality class. Here we propose a spectral explanation for this apparent paradox in two-dimensional active nematic turbulence. The universal energy spectrum $E(q) \sim q^{-1}$ implies sign-field correlations whose decay exponent $a = 3/2$ matches the Weinrib-Halperin marginal threshold $2/ν_0 = 3/2$ for two-dimensional percolation. At this marginal point the long-range correlations are irrelevant under renormalization, so the system flows to the uncorrelated percolation fixed point. Gaussian surrogate fields with the same spectrum confirm $a = 3/2$ to three significant figures, and left-passage analysis of their zero-vorticity interfaces yields $κ= 5.98 \pm 0.08$, consistent with SLE_6. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_16473 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral origin of conformal invariance in active nematic turbulence Redrouthu, Rithvik Soft Condensed Matter Statistical Mechanics Biological Physics Zero-vorticity contours in the collective flows of living cells obey Schramm-Loewner evolution with diffusivity $κ= 6$ and thus fall in the universality class of critical percolation. This observation is surprising because the underlying vorticity field has long-range correlations that, according to the Weinrib-Halperin criterion, should alter the universality class. Here we propose a spectral explanation for this apparent paradox in two-dimensional active nematic turbulence. The universal energy spectrum $E(q) \sim q^{-1}$ implies sign-field correlations whose decay exponent $a = 3/2$ matches the Weinrib-Halperin marginal threshold $2/ν_0 = 3/2$ for two-dimensional percolation. At this marginal point the long-range correlations are irrelevant under renormalization, so the system flows to the uncorrelated percolation fixed point. Gaussian surrogate fields with the same spectrum confirm $a = 3/2$ to three significant figures, and left-passage analysis of their zero-vorticity interfaces yields $κ= 5.98 \pm 0.08$, consistent with SLE_6. |
| title | Spectral origin of conformal invariance in active nematic turbulence |
| topic | Soft Condensed Matter Statistical Mechanics Biological Physics |
| url | https://arxiv.org/abs/2604.16473 |