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The phase-transition in the Vicsek model through Gini index.

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Title: The phase-transition in the Vicsek model through Gini index.
Authors: Kandalam, Ravitheja1 (AUTHOR) ravitheja_kandalam@srmap.edu.in, Das, Soumyaditya1 (AUTHOR) soumyaditya_das@srmap.edu.in, Dey, Supravat1 (AUTHOR) supravat.dey@gmail.com
Source: Physica A. Mar2026, Vol. 685, pN.PAG-N.PAG. 1p.
Subjects: Phase transitions, Gini coefficient, Nonequilibrium thermodynamics, Critical exponents, Finite size scaling (Statistical physics), Statistical mechanics, Dynamical systems
Abstract: At the critical point of a phase transition, the fourth-order Binder cumulant (U), which is a measure of departure from Gaussianity in the order parameter, becomes independent of the system size and obeys a finite-size scaling relation with the correlation length exponent. This feature has been widely used to estimate the critical point and exponents accurately from simulations. Recently, the Gini index, a measure of inequality that traditionally is used in economics to quantify wealth inequality, has been shown to be useful for studying phase transitions in physical systems at equilibrium. By studying phase transition in equilibrium, it has been numerically demonstrated that at the critical point, g in the order parameter becomes independent of the system size and follows a finite-size scaling relation similar to U. Here, we investigate the nonequilibrium phase transition in the Vicsek model of active systems in two dimensions using the index g. For this model, we find that both g and U exhibit similar behavior. For a high self-propelled velocity, both g and U are system size independent at the critical point and obey a finite-size scaling relation for the correlation length exponent. For small self-propulsion, we find the transition is unusual, as there is no single point where g (or U) for various system sizes crosses. [ABSTRACT FROM AUTHOR]
Copyright of Physica A is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
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  Data: The phase-transition in the Vicsek model through Gini index.
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  Data: <searchLink fieldCode="AR" term="%22Kandalam%2C+Ravitheja%22">Kandalam, Ravitheja</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> ravitheja_kandalam@srmap.edu.in</i><br /><searchLink fieldCode="AR" term="%22Das%2C+Soumyaditya%22">Das, Soumyaditya</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> soumyaditya_das@srmap.edu.in</i><br /><searchLink fieldCode="AR" term="%22Dey%2C+Supravat%22">Dey, Supravat</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> supravat.dey@gmail.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Physica+A%22">Physica A</searchLink>. Mar2026, Vol. 685, pN.PAG-N.PAG. 1p.
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  Data: <searchLink fieldCode="DE" term="%22Phase+transitions%22">Phase transitions</searchLink><br /><searchLink fieldCode="DE" term="%22Gini+coefficient%22">Gini coefficient</searchLink><br /><searchLink fieldCode="DE" term="%22Nonequilibrium+thermodynamics%22">Nonequilibrium thermodynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Critical+exponents%22">Critical exponents</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+size+scaling+%28Statistical+physics%29%22">Finite size scaling (Statistical physics)</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+mechanics%22">Statistical mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamical+systems%22">Dynamical systems</searchLink>
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  Data: At the critical point of a phase transition, the fourth-order Binder cumulant (U), which is a measure of departure from Gaussianity in the order parameter, becomes independent of the system size and obeys a finite-size scaling relation with the correlation length exponent. This feature has been widely used to estimate the critical point and exponents accurately from simulations. Recently, the Gini index, a measure of inequality that traditionally is used in economics to quantify wealth inequality, has been shown to be useful for studying phase transitions in physical systems at equilibrium. By studying phase transition in equilibrium, it has been numerically demonstrated that at the critical point, g in the order parameter becomes independent of the system size and follows a finite-size scaling relation similar to U. Here, we investigate the nonequilibrium phase transition in the Vicsek model of active systems in two dimensions using the index g. For this model, we find that both g and U exhibit similar behavior. For a high self-propelled velocity, both g and U are system size independent at the critical point and obey a finite-size scaling relation for the correlation length exponent. For small self-propulsion, we find the transition is unusual, as there is no single point where g (or U) for various system sizes crosses. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of Physica A is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1016/j.physa.2026.131274
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      – Code: eng
        Text: English
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      – SubjectFull: Phase transitions
        Type: general
      – SubjectFull: Gini coefficient
        Type: general
      – SubjectFull: Nonequilibrium thermodynamics
        Type: general
      – SubjectFull: Critical exponents
        Type: general
      – SubjectFull: Finite size scaling (Statistical physics)
        Type: general
      – SubjectFull: Statistical mechanics
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      – SubjectFull: Dynamical systems
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      – TitleFull: The phase-transition in the Vicsek model through Gini index.
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            NameFull: Kandalam, Ravitheja
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            NameFull: Das, Soumyaditya
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            NameFull: Dey, Supravat
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              M: 03
              Text: Mar2026
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              Y: 2026
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