Absence of Phase Transition in the Biswas–Chatterjee–Sen Model on Directed Barabási–Albert Networks

Rodrigues, Talia da Costa; Alencar, David Santana; Alves, Tayroni Alencar; Alves, Gladstone Alencar; Lima, Francisco Welington; Plascak, João Antônio

doi:10.3390/sym18030415

Open AccessArticle

Absence of Phase Transition in the Biswas–Chatterjee–Sen Model on Directed Barabási–Albert Networks

by

Talia da Costa Rodrigues

¹

,

David Santana Alencar

¹,

Tayroni Alencar Alves

¹

,

Gladstone Alencar Alves

²,

Francisco Welington Lima

^1,*

and

João Antônio Plascak

^3,4,5,6,*

¹

Dietrich Stauffer Computational Physics Lab, Departamento de Física, Universidade Federal do Piauí, Teresina 64049-550, PI, Brazil

²

Departamento de Física, Universidade Estadual do Piauí, Teresina 64002-150, PI, Brazil

³

Departamento de Física, Centro de Ciências Exatas e da Natureza, CCEN, Universidade Federal da Paraíba, Cidade Universitária, João Pessoa 58051-970, PB, Brazil

⁴

Departamento de Física, Universidade Federal de Minas Gerais, Belo Horizonte 30123-970, MG, Brazil

⁵

Centro de Desenvolvimento da Tecnologia Nuclear—CDTN, Belo Horizonte 30161-970, MG, Brazil

⁶

Department of Physics and Astronomy, University of Georgia, Athens, GA 30602, USA

^*

Authors to whom correspondence should be addressed.

Symmetry 2026, 18(3), 415; https://doi.org/10.3390/sym18030415

Submission received: 3 February 2026 / Revised: 17 February 2026 / Accepted: 24 February 2026 / Published: 27 February 2026

(This article belongs to the Special Issue Symmetry in Statistical Physics and Nonlinear Phenomena)

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Abstract

The phase transition in the Biswas–Chatterjee–Sen model on directed Barabási–Albert networks has been investigated by means of extensive Monte Carlo simulations with four and fifty neighbors. The relaxation time of the average opinion state of the network and its fourth-order Binder cumulant have been analyzed for several different network sizes. Contrary to what happens on regular lattices, the present results do not show any presence of critical points, or equivalently, an absence of a critical social temperature.

Keywords: phase transition; Biswas–Chatterjee–Sen model; Barabási–Albert networks; Monte Carlo simulations; thermodynamic limit

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MDPI and ACS Style

Rodrigues, T.d.C.; Alencar, D.S.; Alves, T.A.; Alves, G.A.; Lima, F.W.; Plascak, J.A. Absence of Phase Transition in the Biswas–Chatterjee–Sen Model on Directed Barabási–Albert Networks. Symmetry 2026, 18, 415. https://doi.org/10.3390/sym18030415

AMA Style

Rodrigues TdC, Alencar DS, Alves TA, Alves GA, Lima FW, Plascak JA. Absence of Phase Transition in the Biswas–Chatterjee–Sen Model on Directed Barabási–Albert Networks. Symmetry. 2026; 18(3):415. https://doi.org/10.3390/sym18030415

Chicago/Turabian Style

Rodrigues, Talia da Costa, David Santana Alencar, Tayroni Alencar Alves, Gladstone Alencar Alves, Francisco Welington Lima, and João Antônio Plascak. 2026. "Absence of Phase Transition in the Biswas–Chatterjee–Sen Model on Directed Barabási–Albert Networks" Symmetry 18, no. 3: 415. https://doi.org/10.3390/sym18030415

APA Style

Rodrigues, T. d. C., Alencar, D. S., Alves, T. A., Alves, G. A., Lima, F. W., & Plascak, J. A. (2026). Absence of Phase Transition in the Biswas–Chatterjee–Sen Model on Directed Barabási–Albert Networks. Symmetry, 18(3), 415. https://doi.org/10.3390/sym18030415

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Absence of Phase Transition in the Biswas–Chatterjee–Sen Model on Directed Barabási–Albert Networks

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