Numerical investigation of the Brownian 𝑞=2 Potts model
File(s)
Published version
Author(s)
Chen, Letian
Pruessner, Gunnar
Type
Journal Article
Abstract
In active matter, such as the Vicsek model of flocking, particles possess an internal degree of freedom, such as their director, which is subject to interaction with other particles, provided they are within a certain range. In an effort to understand better the interplay between spatial and internal degrees of freedom, we study numerically a variation of the 𝑞=2
Potts model on and off the lattice, where particles are additionally subject to Brownian motion. The lack of a feedback of the internal degrees of freedom to the spatial degrees of freedom renders this model generically nonequilibrium. We confirm previous work that showed that the static exponents of the phase transition are unaffected by the diffusion. In contrast to previous work, we show that the formation of ordered clusters is not undermined by diffusion, but should rather be thought of as an effective form of interaction. We demonstrate how our numerical findings can be understood on the basis of the well-established Model A, B and C: Off lattice, the Brownian 𝑞=2
Potts model is Model C. On the lattice, it is Model A with an additional (irrelevant, conserved) Model B noise.
Potts model on and off the lattice, where particles are additionally subject to Brownian motion. The lack of a feedback of the internal degrees of freedom to the spatial degrees of freedom renders this model generically nonequilibrium. We confirm previous work that showed that the static exponents of the phase transition are unaffected by the diffusion. In contrast to previous work, we show that the formation of ordered clusters is not undermined by diffusion, but should rather be thought of as an effective form of interaction. We demonstrate how our numerical findings can be understood on the basis of the well-established Model A, B and C: Off lattice, the Brownian 𝑞=2
Potts model is Model C. On the lattice, it is Model A with an additional (irrelevant, conserved) Model B noise.
Date Issued
2025-09-01
Date Acceptance
2025-09-05
Citation
Physical Review Research, 2025, 7 (3)
ISSN
2643-1564
Publisher
American Physical Society
Journal / Book Title
Physical Review Research
Volume
7
Issue
3
Copyright Statement
© 2025 The Author(s). Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
License URL
Identifier
10.1103/zdfp-vgwk
Publication Status
Published
Article Number
033295
Date Publish Online
2025-09-29