Spatially patterned phases in a reaction-time-symmetry-broken model of flocking
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909612008013824 |
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| author | Packard, Charles R. Sussman, Daniel M. |
| author_facet | Packard, Charles R. Sussman, Daniel M. |
| contents | We introduce a Vicsek-like flocking model with a minimal form of time-delayed orientational interactions, in which the delays occur on a time scale that is well-separated from other time scales in the model. We achieve this by implementing an ``index-ordered'' update rule, mimicking a scenario in which agents have a distribution of times with which they react to information. This model retains the usual disorder-to-order transition common in flocking models, but we show that it also possesses a second transition, deep in the polar flocking phase, to a state with spatially patterned transverse velocities. We characterize this transition and its sensitivity to finite-size effects using the Binder cumulant, and demonstrate -- via direct measurements and by measuring a susceptibility of the phase to particle index permutations -- that the stability of this phase is directly tied to a subtle spatial organization of a slow-relaxing index-order field. These results highlight the potential for even seemingly insignificant temporal asymmetries to fundamentally alter the collective behavior of active matter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_10657 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spatially patterned phases in a reaction-time-symmetry-broken model of flocking Packard, Charles R. Sussman, Daniel M. Soft Condensed Matter We introduce a Vicsek-like flocking model with a minimal form of time-delayed orientational interactions, in which the delays occur on a time scale that is well-separated from other time scales in the model. We achieve this by implementing an ``index-ordered'' update rule, mimicking a scenario in which agents have a distribution of times with which they react to information. This model retains the usual disorder-to-order transition common in flocking models, but we show that it also possesses a second transition, deep in the polar flocking phase, to a state with spatially patterned transverse velocities. We characterize this transition and its sensitivity to finite-size effects using the Binder cumulant, and demonstrate -- via direct measurements and by measuring a susceptibility of the phase to particle index permutations -- that the stability of this phase is directly tied to a subtle spatial organization of a slow-relaxing index-order field. These results highlight the potential for even seemingly insignificant temporal asymmetries to fundamentally alter the collective behavior of active matter. |
| title | Spatially patterned phases in a reaction-time-symmetry-broken model of flocking |
| topic | Soft Condensed Matter |
| url | https://arxiv.org/abs/2505.10657 |