2026/03/30 by S. Jaroszewicz, Sebastian Jaroszewicz, Nahuel Mendez +4
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Context (archaeology) #Ising model #Opinion Dynamics and Social Influence #Scale (ratio) #Scaling #Spurious relationship #Theoretical and Computational Physics #Work (physics) #cond-mat.stat-mech
paper · pdf · doi:10.1103/23vj-5v8c
published as Phys. Rev. E 114, 014139 2026 · v2: Major revisions. Additional methodological details and clarifications added
arxiv created 2026/03/30 · openalex publication_date 2026/06/29 · openalex created_date 2026/06/30 · openalex updated_date 2026/07/23 · arxiv updated 2026/08/05
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 \citeLudescher2011 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→ 0) in the thermodynamic limit. The method accurately recovers the monofractal exponent of the Ising universality class (α≈ H ≈ 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≈ 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.