Mesoscopic theory of flocking with alignment and anti-alignment copying
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908986114048000 |
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| author | Zheng, Chunming |
| author_facet | Zheng, Chunming |
| contents | We study a stochastic model of collective motion in which individuals update their orientation through pairwise aligning or anti-aligning copying interactions. We analyze both annealed dynamics, where interaction types are chosen probabilistically at each update, and quenched dynamics, where individuals are permanently assigned to aligning or anti-aligning subpopulations. Starting from the microscopic master equation on the circle, we derive an exact mesoscopic description via a Fourier-mode expansion and a systematic large $N$ expansion, obtaining closed Fokker-Planck equations and effective stochastic differential equations for the polarization. We show that competing alignment and anti-alignment suppress long-range polar order in the thermodynamic limit in both cases, while finite systems display nontrivial fluctuation-induced structure controlled by the interaction composition. Our results, validated by Gillespie simulations, establish an analytically tractable framework for collective dynamics characterized by competing copying rules and intrinsic noise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20251 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mesoscopic theory of flocking with alignment and anti-alignment copying Zheng, Chunming Statistical Mechanics Soft Condensed Matter Biological Physics We study a stochastic model of collective motion in which individuals update their orientation through pairwise aligning or anti-aligning copying interactions. We analyze both annealed dynamics, where interaction types are chosen probabilistically at each update, and quenched dynamics, where individuals are permanently assigned to aligning or anti-aligning subpopulations. Starting from the microscopic master equation on the circle, we derive an exact mesoscopic description via a Fourier-mode expansion and a systematic large $N$ expansion, obtaining closed Fokker-Planck equations and effective stochastic differential equations for the polarization. We show that competing alignment and anti-alignment suppress long-range polar order in the thermodynamic limit in both cases, while finite systems display nontrivial fluctuation-induced structure controlled by the interaction composition. Our results, validated by Gillespie simulations, establish an analytically tractable framework for collective dynamics characterized by competing copying rules and intrinsic noise. |
| title | Mesoscopic theory of flocking with alignment and anti-alignment copying |
| topic | Statistical Mechanics Soft Condensed Matter Biological Physics |
| url | https://arxiv.org/abs/2604.20251 |