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Multifractality analysis of phase transition of the two- and three-dimensional XY models

Author

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  • de Sousa, Marcos A.A.
  • de Moura, Francisco A.B.F.
  • Barbosa, Anderson L.R.
  • de Souza, Adauto J.F.

Abstract

We performed an extensive investigation of the multifractal features of time series for magnetization and helicity moduli for the XY model in two and three dimensions. We employed multifractal analysis to extract generalized Hurst exponents and singularity spectra, enabling us to quantify the degree of multifractality across different temperatures. Our results show that multifractality is maximized near the critical points, with broader singularity spectra in the two-dimensional system, which is consistent with the Berezinskii-Kosterlitz-Thouless transition. In three dimensions, the multifractal signatures are sharper and more localized, reflecting the second-order nature of the transition. These findings confirm multifractality as a robust tool that captures essential features of both conventional and topological phase transitions.

Suggested Citation

  • de Sousa, Marcos A.A. & de Moura, Francisco A.B.F. & Barbosa, Anderson L.R. & de Souza, Adauto J.F., 2026. "Multifractality analysis of phase transition of the two- and three-dimensional XY models," Chaos, Solitons & Fractals, Elsevier, vol. 202(P2).
    • Handle: RePEc:eee:chsofr:v:202:y:2026:i:p2:s0960077925015309
    DOI: 10.1016/j.chaos.2025.117517
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    References listed on IDEAS

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    1. Li, Yueling & Dai, Chaoshou, 2006. "A multifractal formalism in a probability space," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 57-73.
    2. Stosic, Borko & Stosic, Tatijana & Tošić, Ivana & Djurdjević, Vladimir, 2025. "Multifractal analysis of temperature in Europe: Climate change effect," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).
    3. Telli, Şahin & Chen, Hongzhuan & Zhao, Xufeng, 2022. "Detecting multifractality and exposing distributions of local fluctuations: Detrended fluctuation analysis with descriptive statistics pooling," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    4. Tsvetkov, V.P. & Mikheev, S.A. & Tsvetkov, I.V. & Derbov, V.L. & Gusev, A.A. & Vinitsky, S.I., 2022. "Modeling the multifractal dynamics of COVID-19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    5. Oliveira, F.M. & Lucena, I.R.A.C. & Ramos, J.G.G.S., 2025. "Multifractal chaos in gravitational waves from binary black hole mergers," Chaos, Solitons & Fractals, Elsevier, vol. 200(P1).
    6. da Silva, Antonio Samuel Alves & Stosic, Tatijana & Arsenić, Ilija & Menezes, Rômulo Simões Cezar & Stosic, Borko, 2023. "Multifractal analysis of standardized precipitation index in Northeast Brazil," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    7. Leal, Fransisco C.B. & Vasconcelos, João V.A. & Negreiros-Neto, Luis G. & de Oliveira, Viviane M. & de Souza, Adauto J.F. & Barbosa, Anderson L.R. & Romaguera, Antonio R. de C., 2024. "Avalanche dynamics of zebrafish schools: Unveiling self-organization and phase transitions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 651(C).
    8. Pastén, Denisse & Pavez-Orrego, Claudia, 2023. "Multifractal time evolution for intraplate earthquakes recorded in southern Norway during 1980–2021," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    9. Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
    10. Achour, Rim & Li, Zhiming & Selmi, Bilel & Wang, Tingting, 2024. "A multifractal formalism for new general fractal measures," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
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