Resolving Spurious Multifractality in Discrete Systems: A Finite-Size Scaling Protocol for MFDFA in the 2D Ising Model
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917371086635008 |
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| author | Jaroszewicz, Sebastian Mendez, Nahuel Beccar-Varela, Maria P. Mariani, Maria Cristina |
| author_facet | Jaroszewicz, Sebastian Mendez, Nahuel Beccar-Varela, Maria P. Mariani, Maria Cristina |
| contents | Multifractal Detrended Fluctuation Analysis (MFDFA) has emerged as a standard tool for characterizing scale invariance in complex systems, yet its application to discrete spin models is frequently marred by reports of ``spurious multifractality'' that contradict established theory. In this work, we resolve this controversy by establishing a rigorous protocol for the analysis of discrete lattice snapshots. Using the 2D Ising model as a benchmark, we demonstrate that the previously reported broad singularity spectra \cite{Ludescher2011} are finite-size artifacts dominated by lattice discreteness effects in the negative moment regime ($q<0$). By restricting the analysis to positive moments and performing a systematic Finite-Size Scaling (FSS) analysis, we show that the spectral width collapses to zero ($Δα\to 0$) in the thermodynamic limit. The method accurately recovers the monofractal exponent of the Ising universality class ($α\approx H \approx 0.875$), consistent with Conformal Field Theory. To validate the discriminatory power of this protocol, we contrast these findings with the Random Bond Ising Model (RBIM), showing that quenched disorder induces a genuine, broad multifractal spectrum ($Δα\approx 0.23$) that survives scaling. Furthermore, we propose a theoretical interpretation where the MFDFA polynomial detrending functions as a phenomenological Renormalization Group filter, suppressing analytic background fields (irrelevant operators) to isolate the singular critical behavior. These results define a robust methodology for distinguishing between clean and disorder-dominated criticality in finite systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04609 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Resolving Spurious Multifractality in Discrete Systems: A Finite-Size Scaling Protocol for MFDFA in the 2D Ising Model Jaroszewicz, Sebastian Mendez, Nahuel Beccar-Varela, Maria P. Mariani, Maria Cristina Statistical Mechanics Multifractal Detrended Fluctuation Analysis (MFDFA) has emerged as a standard tool for characterizing scale invariance in complex systems, yet its application to discrete spin models is frequently marred by reports of ``spurious multifractality'' that contradict established theory. In this work, we resolve this controversy by establishing a rigorous protocol for the analysis of discrete lattice snapshots. Using the 2D Ising model as a benchmark, we demonstrate that the previously reported broad singularity spectra \cite{Ludescher2011} are finite-size artifacts dominated by lattice discreteness effects in the negative moment regime ($q<0$). By restricting the analysis to positive moments and performing a systematic Finite-Size Scaling (FSS) analysis, we show that the spectral width collapses to zero ($Δα\to 0$) in the thermodynamic limit. The method accurately recovers the monofractal exponent of the Ising universality class ($α\approx H \approx 0.875$), consistent with Conformal Field Theory. To validate the discriminatory power of this protocol, we contrast these findings with the Random Bond Ising Model (RBIM), showing that quenched disorder induces a genuine, broad multifractal spectrum ($Δα\approx 0.23$) that survives scaling. Furthermore, we propose a theoretical interpretation where the MFDFA polynomial detrending functions as a phenomenological Renormalization Group filter, suppressing analytic background fields (irrelevant operators) to isolate the singular critical behavior. These results define a robust methodology for distinguishing between clean and disorder-dominated criticality in finite systems. |
| title | Resolving Spurious Multifractality in Discrete Systems: A Finite-Size Scaling Protocol for MFDFA in the 2D Ising Model |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2603.04609 |