The DOI matches its Crossref record; 6 of the 6 references it cites were found in a registry or an index.
Long-Range Order in a Two-Dimensional DynamicalXYModel: How Birds Fly Together
Abstract
We propose a nonequilibrium continuum dynamical model for the collective motion of large groups of biological organisms (e.g., flocks of birds, slime molds, etc.) Our model becomes highly nontrivial, and different from the equilibrium model, for $d<{d}_{c}=4$; nonetheless, we are able to determine its scaling exponents exactly in $d=2$ and show that, unlike equilibrium systems, our model exhibits a broken continuous symmetry even in $d=2$. Our model describes a large universality class of microscopic rules, including those recently simulated by Vicsek et al.
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Cites
Ordering, metastability and phase transitions in two-dimensional systems
Kosterlitz, J. M., & Thouless, D. J. (1973) · Journal of Physics C: Solid State Physics · doi:10.1088/0022-3719/6/7/010 · Cited by 9,538
Mermin, N. D., & Wagner, H. (1966) · Physical Review Letters · doi:10.1103/physrevlett.17.1133 · Cited by 8,363
Novel Type of Phase Transition in a System of Self-Driven Particles
Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I., & Shochet, O. (1995) · Physical Review Letters · doi:10.1103/physrevlett.75.1226 · Cited by 7,380
Flocks, herds and schools: A distributed behavioral model
Reynolds, C. W. (1987) · ACM SIGGRAPH Computer Graphics · doi:10.1145/37402.37406 · Cited by 5,148
Large-distance and long-time properties of a randomly stirred fluid
Forster, D., Nelson, D. R., & Stephen, M. J. (1977) · Physical Review A · doi:10.1103/physreva.16.732 · Cited by 1,352
Collective patterns and decision-making
Deneubourg, J. L., & Goss, S. (1989) · Ethology Ecology & Evolution · doi:10.1080/08927014.1989.9525500 · Cited by 672
Cited by
Coordination of groups of mobile autonomous agents using nearest neighbor rules
Jadbabaie, A., Lin, J., & Morse, A. S. (2003) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2003.812781 · Cited by 8,339
Statistical physics of social dynamics
Castellano, C., Fortunato, S., & Loreto, V. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.591 · Cited by 4,119
Traffic and related self-driven many-particle systems
Helbing, D. (2001) · Reviews of Modern Physics · doi:10.1103/revmodphys.73.1067 · Cited by 3,245
Vicsek, T., & Zafeiris, A. (2012) · Physics Reports · doi:10.1016/j.physrep.2012.03.004 · Cited by 2,923
Flocks, herds, and schools: A quantitative theory of flocking
Toner, J., & Tu, Y. (1998) · Physical Review E · doi:10.1103/physreve.58.4828 · Cited by 1,626
Self-citation
Metadata
- Authors
- Toner, J., & Tu, Y.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1995-12-04
- Volume
- 75
- Issue
- 23
- Pages
- 4326-4329
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2063134919
- Cited by
- 1,243
- References
- 6
- FWCI
- 4.00
- Type
- journal article
- Language
- en
- Open access
- closed
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
