%0 Journal Article %1 Toner1995 %A Toner, John %A Tu, Yuhai %D 1995 %I American Physical Society %J Physical Review Letters %K animal-groups collective-motion correlations phase-transition swarms %N 23 %P 4326--4329 %R 10.1103/PhysRevLett.75.4326 %T Long-Range Order in a Two-Dimensional Dynamical $XY$ Model: How Birds Fly Together %V 75 %X 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<dc=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.

@article{Toner1995, 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<dc=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.}, added-at = {2011-05-18T13:50:33.000+0200}, author = {Toner, John and Tu, Yuhai}, biburl = {https://www.bibsonomy.org/bibtex/283aa9ff374fc2f0232d804f2bec01ab4/rincedd}, doi = {10.1103/PhysRevLett.75.4326}, interhash = {0cd55d5e337f5e0e4ca53a1a50fbb1fb}, intrahash = {83aa9ff374fc2f0232d804f2bec01ab4}, journal = {Physical Review Letters}, keywords = {animal-groups collective-motion correlations phase-transition swarms}, number = 23, pages = {4326--4329}, publisher = {American Physical Society}, timestamp = {2011-05-18T13:50:33.000+0200}, title = {Long-Range Order in a Two-Dimensional Dynamical $XY$ Model: How Birds Fly Together}, volume = 75, year = 1995 }