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

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

Chaos, Solitons & Fractals, 2026, vol. 202, issue P2

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.

Keywords: XY model; Multifractality; Phase transition; Hurst exponent; Singularity spectrum (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:202:y:2026:i:p2:s0960077925015309

DOI: 10.1016/j.chaos.2025.117517

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