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arxiv: 2605.09743 · v1 · submitted 2026-05-10 · ❄️ cond-mat.stat-mech

Recognition: no theorem link

Equilibrium and non-equilibrium properties of active matter systems

Mintu Karmakar

Authors on Pith no claims yet

Pith reviewed 2026-05-12 03:28 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech
keywords active matterself-propelled particlesmotility-induced phase separationjammingkinetic arrestphase transitionscollective behavior
0
0 comments X

The pith

Active particle systems form jams, phases, and flocks when noise, velocity, exclusion, and disorder are varied.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper reviews how self-propelled particles in active matter respond to thermal noise, propulsion speed, external fields, volume exclusion, and media disorder. These factors produce collective phenomena including flocking transitions, motility-induced phase separation, jamming, kinetic arrest, and various phase transitions. The review examines both lattice and off-lattice models, with emphasis on spin anisotropy and volume exclusion to capture the dynamics. A sympathetic reader would care because the same parameters appear in real biological and engineered systems where collective motion determines function. The central object carrying the argument is the family of active-matter models that incorporate these ingredients.

Core claim

In active matter systems, the collective behavior of self-propelled particles is controlled by system parameters including thermal noise, self-propulsion velocity, external field strength, volume exclusion, and disorder in the media, which together produce jamming, kinetic arrest, motility-induced phase separation, coexisting phases, microphase separation, and phase transitions.

What carries the argument

Active-matter models that combine volume exclusion with spin anisotropy on and off lattice, which encode the competition between self-propulsion, steric repulsion, and orientational alignment.

If this is right

  • Raising self-propulsion velocity while holding density fixed drives motility-induced phase separation into dense and dilute regions.
  • Introducing quenched disorder in the medium produces kinetic arrest and jamming even at moderate densities.
  • An external aligning field can suppress or enhance flocking transitions depending on its strength relative to noise.
  • Volume exclusion combined with spin anisotropy stabilizes microphase separation instead of bulk phase separation in off-lattice geometries.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same parameter knobs could be used to design synthetic active materials whose macroscopic flow or clustering can be switched by external fields or added obstacles.
  • Biological systems such as migrating cell sheets or bacterial biofilms may achieve similar collective states by tuning effective noise or propulsion without invoking new interaction rules.
  • Extending the models to include hydrodynamic interactions or shape anisotropy would test whether the reported phases survive once long-range fluid flows are added.

Load-bearing premise

Standard active-matter models that include volume exclusion and spin anisotropy already contain the essential mechanisms needed to explain the observed collective phenomena.

What would settle it

A controlled experiment on colloidal or bacterial active matter in which increasing self-propulsion velocity or added disorder fails to produce the predicted shift from uniform motion to phase-separated or arrested states.

read the original abstract

Active matter systems encompass both natural and artificially created systems consisting of numerous active particles. These particles actively consume energy to propel themselves or exert mechanical forces, leading to intricate behaviors and a diverse range of collective motions from flocking transition to motility-induced phase separation. The flocking transition refers to the spontaneous alignment and coordination of individuals in a group, resembling the cohesive motion observed in flocks of birds or schools of fish. On the other hand, motility-induced phase separation refers to the segregation of active particles into distinct regions based on their differing motility levels. In this presentation, I will talk about active matter systems, specifically focusing on the collective behavior and dynamics, including the influence of volume exclusion features, the impact of disorder in the media, and the behavior of self-propelled particles in off-lattice domains by introducing spin anisotropy. The objective is to understand how the collective behavior of self-propelled particles is affected by various system parameters, including thermal noise, self-propulsion velocity, external field strength, etc. I will furthermore show the phenomena such as jamming, kinetic arrest, motility-induced phase separation, coexisting phases, microphase separation, and phase transitions within the context of active matter models.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript is an abstract for a presentation on active matter systems. It describes collective behaviors of self-propelled particles, including flocking transitions and motility-induced phase separation (MIPS). It outlines the influence of parameters such as thermal noise, self-propulsion velocity, external field strength, volume exclusion, disorder in the media, and spin anisotropy on phenomena including jamming, kinetic arrest, coexisting phases, microphase separation, and phase transitions. The text emphasizes understanding these effects in both on- and off-lattice models but provides no equations, derivations, simulation details, or quantitative results.

Significance. The described phenomena are well-established in the active matter literature, so the summary adds little new insight or predictive power even if the underlying models are sound. No machine-checked proofs, reproducible code, parameter-free derivations, or falsifiable predictions are present. The work functions as a high-level overview rather than an advance that would shift consensus or enable new calculations.

major comments (2)
  1. The central claims (e.g., that thermal noise, self-propulsion velocity, and volume exclusion control jamming and MIPS) are stated descriptively without any supporting model definition, equation, or result. No section, equation, or table exists to evaluate whether the stated parameter dependences follow from a specific Hamiltonian or simulation protocol.
  2. The manuscript presents no original quantitative claim, derivation, or data set. All listed phenomena (flocking, MIPS, jamming, kinetic arrest) are standard consensus results; the text therefore contains no load-bearing assertion that can be verified or falsified within the provided scope.
minor comments (2)
  1. The text is written in first-person presentation style ('I will talk about', 'I will furthermore show') rather than the impersonal style expected for a journal article.
  2. No references, model equations, or figure captions are supplied, making it impossible to trace the specific active-matter models invoked.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their comments on our manuscript. We clarify at the outset that this submission is an abstract for a presentation rather than a full research article; its purpose is to outline the topics and scope of the talk on collective dynamics in active matter. We address the major comments below in a point-by-point manner.

read point-by-point responses
  1. Referee: The central claims (e.g., that thermal noise, self-propulsion velocity, and volume exclusion control jamming and MIPS) are stated descriptively without any supporting model definition, equation, or result. No section, equation, or table exists to evaluate whether the stated parameter dependences follow from a specific Hamiltonian or simulation protocol.

    Authors: We agree that the abstract contains no equations, model Hamiltonians, or quantitative results. This is intentional, as the document is a concise presentation abstract whose role is to describe the phenomena and parameters that will be discussed in the talk (including on- and off-lattice models, volume exclusion, disorder, and spin anisotropy). Detailed model definitions, simulation protocols, and supporting derivations are reserved for the oral presentation itself. If the venue requires it, we are willing to append a brief sentence referencing standard models from the literature (e.g., Vicsek-type or active Brownian particle models) to indicate the framework. revision: partial

  2. Referee: The manuscript presents no original quantitative claim, derivation, or data set. All listed phenomena (flocking, MIPS, jamming, kinetic arrest) are standard consensus results; the text therefore contains no load-bearing assertion that can be verified or falsified within the provided scope.

    Authors: We acknowledge that the individual phenomena listed are established in the active-matter literature. The abstract does not claim new quantitative results or falsifiable predictions; its intent is to indicate the specific parameter regimes and model variants (thermal noise, self-propulsion velocity, external fields, media disorder, spin anisotropy) that the presentation will examine in both equilibrium and non-equilibrium contexts. This focused synthesis may still be of interest to attendees even though no novel data or derivations appear in the abstract text. revision: no

Circularity Check

0 steps flagged

No significant circularity; presentation summarizes established results

full rationale

The document is a presentation abstract that restates well-known active-matter phenomena (flocking, MIPS, jamming, kinetic arrest) and lists standard parameters (thermal noise, self-propulsion speed, volume exclusion, disorder, spin anisotropy) known to influence them. No original model equations, derivations, fitted parameters, or quantitative predictions are advanced. Consequently no load-bearing step reduces by construction to a self-definition, a fitted input renamed as prediction, or a self-citation chain. The text is self-contained as a survey of consensus knowledge.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No mathematical content, free parameters, or new entities are introduced in the abstract; the text is purely descriptive of existing models and phenomena.

pith-pipeline@v0.9.0 · 5499 in / 939 out tokens · 48844 ms · 2026-05-12T03:28:44.064982+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

300 extracted references · 300 canonical work pages

  1. [1]

    author author M. C. \ Marchetti , author J. F. \ Joanny , author S. Ramaswamy , author T. B. \ Liverpool , author J. Prost , author M. Rao , \ and\ author R. A. \ Simha ,\ @noop journal journal Rev. Mod. Phys. \ volume 85 ,\ pages 1143 ( year 2013 ) NoStop

  2. [2]

    author author M. R. \ Shaebani , author A. Wysocki , author R. G. \ Winkler , author G. Gompper , \ and\ author H. Rieger ,\ @noop journal journal Nat. Rev. Phys. \ volume 2 ,\ pages 181 ( year 2020 ) NoStop

  3. [3]

    Bottinelli , author D

    author author A. Bottinelli , author D. T. J. \ Sumpter , \ and\ author J. L. \ Silverberg ,\ @noop journal journal Phys. Rev. Lett. \ volume 117 ,\ pages 228301 ( year 2016 ) NoStop

  4. [4]

    Helbing \ and\ author P

    author author D. Helbing \ and\ author P. Molnar ,\ @noop journal journal Phys. Rev. E \ volume 51 ,\ pages 4282 ( year 1995 ) NoStop

  5. [5]

    Garcimart \' n , author J

    author author A. Garcimart \' n , author J. M. \ Pastor , author L. M. \ Ferrer , author J. J. \ Ramos , author C. Mart \' n-G \'o mez , \ and\ author I. Zuriguel ,\ @noop journal journal Phys. Rev. E \ volume 91 ,\ pages 022808 ( year 2015 ) NoStop

  6. [6]

    Ballerini , author N

    author author M. Ballerini , author N. Cabibbo , author R. Candelier , author A. Cavagna , author E. Cisbani , author I. Giardina , author V. Lecomte , author A. Orlandi , author G. Parisi , author A. Procaccini , et al. ,\ @noop journal journal Proc. Nat. Acad. Sci. \ volume 105 ,\ pages 1232 ( year 2008 ) NoStop

  7. [7]

    Becco , author N

    author author C. Becco , author N. Vandewalle , author J. Delcourt , \ and\ author P. Poncin ,\ @noop journal journal Physica A \ volume 367 ,\ pages 487 ( year 2006 ) NoStop

  8. [8]

    author author D. S. \ Calovi , author U. Lopez , author S. Ngo , author C. Sire , author H. Chat \'e , \ and\ author G. Theraulaz ,\ @noop journal journal New J. Phys. \ volume 16 ,\ pages 015026 ( year 2014 ) NoStop

  9. [9]

    author author E. B. \ Steager , author C.-B. \ Kim , \ and\ author M. J. \ Kim ,\ @noop journal journal Physics of Fluids \ volume 20 ( year 2008 ) NoStop

  10. [10]

    Peruani , author J

    author author F. Peruani , author J. Starru , author V. Jakovljevic , author L. S gaard-Andersen , author A. Deutsch , \ and\ author M. B \"a r ,\ @noop journal journal Phys. Rev. Lett. \ volume 108 ,\ pages 098102 ( year 2012 ) NoStop

  11. [11]

    Giavazzi , author M

    author author F. Giavazzi , author M. Paoluzzi , author M. Macchi , author D. Bi , author G. Scita , author M. L. \ Manning , author R. Cerbino , \ and\ author M. C. \ Marchetti ,\ @noop journal journal Soft Matter \ volume 14 ,\ pages 3471 ( year 2018 ) NoStop

  12. [12]

    Schaller , author C

    author author V. Schaller , author C. Weber , author C. Semmrich , author E. Frey , \ and\ author A. R. \ Bausch ,\ @noop journal journal Nature \ volume 467 ,\ pages 73 ( year 2010 ) NoStop

  13. [13]

    Sumino , author K

    author author Y. Sumino , author K. H. \ Nagai , author Y. Shitaka , author D. Tanaka , author K. Yoshikawa , author H. Chat \'e , \ and\ author K. Oiwa ,\ @noop journal journal Nature \ volume 483 ,\ pages 448 ( year 2012 ) NoStop

  14. [14]

    Sanchez , author D

    author author T. Sanchez , author D. T. N. \ Chen , author S. J. \ DeCamp , author M. Heymann , \ and\ author Z. Dogic ,\ @noop journal journal Nature \ volume 491 ,\ pages 431 ( year 2012 ) NoStop

  15. [15]

    Vicsek , author A

    author author T. Vicsek , author A. Czir \'o k , author E. Ben-Jacob , author I. Cohen , \ and\ author O. Shochet ,\ @noop journal journal Phys. Rev. Lett. \ volume 75 ,\ pages 1226 ( year 1995 ) NoStop

  16. [16]

    Toner \ and\ author Y

    author author J. Toner \ and\ author Y. Tu ,\ @noop journal journal Phys. Rev. Lett. \ volume 75 ,\ pages 4326 ( year 1995 ) NoStop

  17. [17]

    Toner \ and\ author Y

    author author J. Toner \ and\ author Y. Tu ,\ @noop journal journal Phys. Rev. E \ volume 58 ,\ pages 4828 ( year 1998 ) NoStop

  18. [18]

    Toner ,\ @noop journal journal Phys

    author author J. Toner ,\ @noop journal journal Phys. Rev. E \ volume 86 ,\ pages 031918 ( year 2012 ) NoStop

  19. [19]

    author author A. P. \ Solon , author H. Chat \'e , \ and\ author J. Tailleur ,\ @noop journal journal Phys. Rev. Lett. \ volume 114 ,\ pages 068101 ( year 2015 a ) NoStop

  20. [20]

    Gr \'e goire \ and\ author H

    author author G. Gr \'e goire \ and\ author H. Chat \'e ,\ @noop journal journal Phys. Rev. Lett. \ volume 92 ,\ pages 025702 ( year 2004 ) NoStop

  21. [21]

    author author A. P. \ Solon , author J. B. \ Caussin , author D. Bartolo , author H. Chat \'e , \ and\ author J. Tailleur ,\ @noop journal journal Phys. Rev. E \ volume 92 ,\ pages 062111 ( year 2015 b ) NoStop

  22. [22]

    K \"u rsten \ and\ author T

    author author R. K \"u rsten \ and\ author T. Ihle ,\ @noop journal journal Phys. Rev. Lett. \ volume 125 ,\ pages 188003 ( year 2020 ) NoStop

  23. [23]

    Peruani , author T

    author author F. Peruani , author T. Klauss , author A. Deutsch , \ and\ author A. Voss-Boehme ,\ @noop journal journal Phys. Rev. Lett. \ volume 106 ,\ pages 128101 ( year 2011 ) NoStop

  24. [24]

    author author A. P. \ Solon \ and\ author J. Tailleur ,\ @noop journal journal Phys. Rev. Lett. \ volume 111 ,\ pages 078101 ( year 2013 ) NoStop

  25. [25]

    author author A. P. \ Solon \ and\ author J. Tailleur ,\ @noop journal journal Phys. Rev. E \ volume 92 ,\ pages 042119 ( year 2015 ) NoStop

  26. [26]

    Ishibashi \ and\ author H

    author author K. Ishibashi \ and\ author H. Sakaguchi ,\ @noop journal journal J. Phys. Soc. Jpn. \ volume 91 ,\ pages 034003 ( year 2022 ) NoStop

  27. [27]

    Chatterjee , author M

    author author S. Chatterjee , author M. Mangeat , author R. Paul , \ and\ author H. Rieger ,\ @noop journal journal EPL \ volume 130 ,\ pages 66001 ( year 2020 ) NoStop

  28. [28]

    Mangeat , author S

    author author M. Mangeat , author S. Chatterjee , author R. Paul , \ and\ author H. Rieger ,\ @noop journal journal Phys. Rev. E \ volume 102 ,\ pages 042601 ( year 2020 ) NoStop

  29. [29]

    Chatterjee , author M

    author author S. Chatterjee , author M. Mangeat , \ and\ author H. Rieger ,\ @noop journal journal EPL \ volume 138 ,\ pages 41001 ( year 2022 ) NoStop

  30. [30]

    Solon , author H

    author author A. Solon , author H. Chat \'e , author J. Toner , \ and\ author J. Tailleur ,\ @noop journal journal Phys. Rev. Lett. \ volume 128 ,\ pages 208004 ( year 2022 ) NoStop

  31. [31]

    Romanczuk , author M

    author author P. Romanczuk , author M. B \"a r , author W. Ebeling , author B. Lindner , \ and\ author L. Schimansky-Geier ,\ @noop journal journal Eur. Phys. J. Special Topics \ volume 202 ,\ pages 1 ( year 2012 ) NoStop

  32. [32]

    author author M. E. \ Cates \ and\ author J. Tailleur ,\ @noop journal journal Annu. Rev. Condens. Matter Phys. \ volume 6 ,\ pages 219 ( year 2015 ) NoStop

  33. [33]

    Gr \'e goire , author H

    author author G. Gr \'e goire , author H. Chat \'e , \ and\ author Y. Tu ,\ @noop journal journal Physica D \ volume 181 ,\ pages 157 ( year 2003 ) NoStop

  34. [34]

    Mart \' n-G \'o mez , author D

    author author A. Mart \' n-G \'o mez , author D. Levis , author A. D \' az-Guilera , \ and\ author I. Pagonabarraga ,\ @noop journal journal Soft Matter \ volume 14 ,\ pages 2610 ( year 2018 ) NoStop

  35. [35]

    Sese-Sansa , author I

    author author E. Sese-Sansa , author I. Pagonabarraga , \ and\ author D. Levis ,\ @noop journal journal EPL \ volume 124 ,\ pages 30004 ( year 2018 ) NoStop

  36. [36]

    Berthier , author E

    author author L. Berthier , author E. Flenner , \ and\ author G. Szamel ,\ @noop journal journal J. Chem. Phys. \ volume 150 ( year 2019 ) NoStop

  37. [37]

    Kourbane-Houssene , author C

    author author M. Kourbane-Houssene , author C. Erignoux , author T. Bodineau , \ and\ author J. Tailleur ,\ @noop journal journal Phys. Rev. Lett. \ volume 120 ,\ pages 268003 ( year 2018 ) NoStop

  38. [38]

    author author A. N. \ Kolmogorov ,\ @noop journal journal Math. Ann. \ volume 112 ,\ pages 155 ( year 1936 ) NoStop

  39. [39]

    author author A. J. \ Liu \ and\ author S. R. \ Nagel ,\ @noop journal journal Annu. Rev. Condens. Matter Phys. \ volume 1 ,\ pages 347 ( year 2010 ) NoStop

  40. [40]

    Digregorio , author D

    author author P. Digregorio , author D. Levis , author A. Suma , author L. F. \ Cugliandolo , author G. Gonnella , \ and\ author I. Pagonabarraga ,\ @noop journal journal Phys. Rev. Lett. \ volume 121 ,\ pages 098003 ( year 2018 ) NoStop

  41. [41]

    author author M. N. \ Van Der Linden , author L. C. \ Alexander , author D. G. A. L. \ Aarts , \ and\ author O. Dauchot ,\ @noop journal journal Phys. Rev. Lett. \ volume 123 ,\ pages 098001 ( year 2019 ) NoStop

  42. [42]

    author author C. B. \ Caporusso , author P. Digregorio , author D. Levis , author L. F. \ Cugliandolo , \ and\ author G. Gonnella ,\ @noop journal journal Phys. Rev. Lett. \ volume 125 ,\ pages 178004 ( year 2020 ) NoStop

  43. [43]

    Geyer , author D

    author author D. Geyer , author D. Martin , author J. Tailleur , \ and\ author D. Bartolo ,\ @noop journal journal Phys. Rev. X \ volume 9 ,\ pages 031043 ( year 2019 ) NoStop

  44. [44]

    Ses \'e -Sansa , author D

    author author E. Ses \'e -Sansa , author D. Levis , \ and\ author I. Pagonabarraga ,\ @noop journal journal Physical Review E \ volume 104 ,\ pages 054611 ( year 2021 ) NoStop

  45. [45]

    Levis , author J

    author author D. Levis , author J. Codina , \ and\ author I. Pagonabarraga ,\ @noop journal journal Soft Matter \ volume 13 ,\ pages 8113 ( year 2017 ) NoStop

  46. [46]

    author author B. S. \ Kerner \ and\ author H. Rehborn ,\ @noop journal journal Phys. Rev. Lett. \ volume 79 ,\ pages 4030 ( year 1997 ) NoStop

  47. [47]

    Henkes , author Y

    author author S. Henkes , author Y. Fily , \ and\ author M. C. \ Marchetti ,\ @noop journal journal Phys. Rev. E \ volume 84 ,\ pages 040301 ( year 2011 ) NoStop

  48. [48]

    Hecht ,\ @noop journal journal J

    author author F. Hecht ,\ @noop journal journal J. Numer. Math. \ volume 20 ,\ pages 251 ( year 2012 ) NoStop

  49. [49]

    author author O. C. \ Zienkiewicz , author R. L. \ Taylor , author P. Nithiarasu , \ and\ author J. Z. \ Zhu ,\ @noop journal journal Chap \ volume 6 ,\ pages 96 ( year 1977 ) NoStop

  50. [50]

    Karmakar , author S

    author author M. Karmakar , author S. Chatterjee , author M. Mangeat , author H. Rieger , \ and\ author R. Paul ,\ https://doi.org/10.5281/zenodo.7942534 journal journal Zendo \ ( year 2023 ),\ https://doi.org/10.5281/zenodo.7942534 NoStop

  51. [51]

    Weinrib \ and\ author B

    author author A. Weinrib \ and\ author B. I. \ Halperin ,\ @noop journal journal Phys. Rev. B \ volume 27 ,\ pages 413 ( year 1983 ) NoStop

  52. [52]

    author author V. S. \ Dotsenko ,\ @noop journal journal Physics-Uspekhi \ volume 38 ,\ pages 457 ( year 1995 ) NoStop

  53. [53]

    Kumar , author S

    author author M. Kumar , author S. Chatterjee , author R. Paul , \ and\ author S. Puri ,\ @noop journal journal Phys. Rev. E \ volume 96 ,\ pages 042127 ( year 2017 ) NoStop

  54. [54]

    Forg \'a cs , author A

    author author P. Forg \'a cs , author A. Lib \'a l , author C. Reichhardt , \ and\ author C. J. O. \ Reichhardt ,\ @noop journal journal Phys. Rev. E \ volume 104 ,\ pages 044613 ( year 2021 ) NoStop

  55. [55]

    Reichhardt \ and\ author C

    author author C. Reichhardt \ and\ author C. J. O. \ Reichhardt ,\ @noop journal journal Phys. Rev. E \ volume 90 ,\ pages 012701 ( year 2014 ) NoStop

  56. [56]

    Karmakar , author S

    author author M. Karmakar , author S. Chatterjee , author H. Rieger , \ and\ author R. Paul ,\ @noop title Disorder active potts model , \ ( year unpublished ) NoStop

  57. [57]

    Merrigan , author K

    author author C. Merrigan , author K. Ramola , author R. Chatterjee , author N. Segall , author Y. Shokef , \ and\ author B. Chakraborty ,\ @noop journal journal Phys. Rev. R. \ volume 2 ,\ pages 013260 ( year 2020 ) NoStop

  58. [58]

    Caprini , author U

    author author L. Caprini , author U. M. B. \ Marconi , \ and\ author A. Puglisi ,\ @noop journal journal Phys. Rev. Lett. \ volume 124 ,\ pages 078001 ( year 2020 ) NoStop

  59. [59]

    author author F. D. C. \ Farrell , author M. C. \ Marchetti , author D. Marenduzzo , \ and\ author J. Tailleur ,\ @noop journal journal Phys. Rev. Lett. \ volume 108 ,\ pages 248101 ( year 2012 ) NoStop

  60. [60]

    Toner , author Y

    author author J. Toner , author Y. Tu , \ and\ author S. Ramaswamy ,\ @noop journal journal Annals of Physics \ volume 318 ,\ pages 170 ( year 2005 ) NoStop

  61. [61]

    Juelicher , author K

    author author F. Juelicher , author K. Kruse , author J. Prost , \ and\ author J.-F. \ Joanny ,\ @noop journal journal Phys. Rep. \ volume 449 ,\ pages 3 ( year 2007 ) NoStop

  62. [62]

    \ Joanny \ and\ author J

    author author J.-F. \ Joanny \ and\ author J. Prost ,\ @noop journal journal HFSP J \ volume 3 ,\ pages 94 ( year 2009 ) NoStop

  63. [63]

    Ramaswamy ,\ @noop journal journal Annu

    author author S. Ramaswamy ,\ @noop journal journal Annu. Rev. Condens. Matter Phys. \ volume 1 ,\ pages 323 ( year 2010 ) NoStop

  64. [64]

    author author A. P. \ Solon \ and\ author J. Tailleur ,\ @noop journal journal Phys. Rev. Lett. \ volume 111 ,\ pages 078101 ( year 2013 a ) NoStop

  65. [65]

    Chatterjee , author M

    author author S. Chatterjee , author M. Mangeat , author R. Paul , \ and\ author H. Rieger ,\ @noop journal journal EPL \ volume 130 ,\ pages 66001 ( year 2020 a ) NoStop

  66. [66]

    Peled , author S

    author author S. Peled , author S. D. \ Ryan , author S. Heidenreich , author M. B \"a r , author G. Ariel , \ and\ author A. Be'Er ,\ @noop journal journal Phys. Rev. E \ volume 103 ,\ pages 032413 ( year 2021 ) NoStop

  67. [67]

    Chatterjee , author M

    author author S. Chatterjee , author M. Mangeat , author C. U. \ Woo , author H. Rieger , \ and\ author J. D. \ Noh ,\ @noop journal journal Phys. Rev. E \ volume 107 ,\ pages 024607 ( year 2023 ) NoStop

  68. [68]

    Metropolis , author A

    author author N. Metropolis , author A. W. \ Rosenbluth , author M. N. \ Rosenbluth , author A. H. \ Teller , \ and\ author E. Teller ,\ @noop journal journal J. Chem. Phys. \ volume 21 ,\ pages 1087 ( year 1953 ) NoStop

  69. [69]

    author author M. E. J. \ Newman \ and\ author G. Barkema ,\ @noop title Monte Carlo methods in statistical physics \ ( publisher Clarendon Press ,\ year 1999 ) NoStop

  70. [70]

    Landau \ and\ author K

    author author D. Landau \ and\ author K. Binder ,\ @noop title A guide to Monte Carlo simulations in statistical physics \ ( publisher Cambridge university press ,\ year 2021 ) NoStop

  71. [71]

    Romanczuk , author M

    author author P. Romanczuk , author M. B \"a r , author W. Ebeling , author B. Lindner , \ and\ author L. Schimansky-Geier ,\ @noop journal journal The European Physical Journal Special Topics \ volume 202 ,\ pages 1 ( year 2012 ) NoStop

  72. [72]

    Ses \'e -Sansa , author D

    author author E. Ses \'e -Sansa , author D. Levis , \ and\ author I. Pagonabarraga ,\ @noop journal journal Phys. Rev. E \ volume 104 ,\ pages 054611 ( year 2021 ) NoStop

  73. [73]

    Chepizhko , author E

    author author O. Chepizhko , author E. G. \ Altmann , \ and\ author F. Peruani ,\ @noop journal journal Phys. Rev. Lett. \ volume 110 ,\ pages 238101 ( year 2013 ) NoStop

  74. [74]

    Toner , author N

    author author J. Toner , author N. Guttenberg , \ and\ author Y. Tu ,\ @noop journal journal Phys. Rev. E \ volume 98 ,\ pages 062604 ( year 2018 a ) NoStop

  75. [75]

    Toner , author N

    author author J. Toner , author N. Guttenberg , \ and\ author Y. Tu ,\ @noop journal journal Phys. Rev. Lett. \ volume 121 ,\ pages 248002 ( year 2018 b ) NoStop

  76. [76]

    Das , author M

    author author R. Das , author M. Kumar , \ and\ author S. Mishra ,\ @noop journal journal Phys. Rev. E \ volume 98 ,\ pages 060602 ( year 2018 ) NoStop

  77. [77]

    Codina , author B

    author author J. Codina , author B. Mahault , author H. Chat \'e , author J. Dobnikar , author I. Pagonabarraga , \ and\ author X. Shi ,\ @noop journal journal Phys. Rev. Lett. \ volume 128 ,\ pages 218001 ( year 2022 ) NoStop

  78. [78]

    author author A. P. \ Solon \ and\ author J. Tailleur ,\ @noop journal journal Physical Review Letters \ volume 111 ,\ pages 078101 ( year 2013 b ) NoStop

  79. [79]

    Karmakar , author S

    author author M. Karmakar , author S. Chatterjee , author M. Mangeat , author H. Rieger , \ and\ author R. Paul ,\ @noop journal journal Physical Review E \ volume 108 ,\ pages 014604 ( year 2023 ) NoStop

  80. [80]

    author author A. J. \ Bray ,\ @noop journal journal Advances in Physics \ volume 51 ,\ pages 481 ( year 2002 ) NoStop

Showing first 80 references.