Finite-size scaling to resolve spurious multifractality in the two-dimensional Ising model
S. Jaroszewicz, Nahuel Daniel Mendez, Maria Pia Beccar-Varela +1 more
Multifractal detrended fluctuation analysis 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 two-dimensional Ising model as a benchmark, we demonstrate that the previously reported broad singularity spectra 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. Applying this FSS protocol to the random bond Ising model, we reveal that the broad multifractal dispersion often attributed to quenched disorder also flattens systematically with increasing system size. These results demonstrate that apparent multifractality in finite discrete lattices is predominantly driven by preasymptotic discreteness artifacts, underscoring the universal necessity of FSS to avoid false positives in statistical mechanics.
arXiv:2603.04609•Physical review. E•Jun 29, 2026•0 citations