arXiv subjects

Nahuel Mendez

Publications and source records attributed to Nahuel Mendez.

5 recordsLinked to original sources

arXiv2026

Two temperature scales in the Ising model on the $\{5,4\}$ hyperbolic lattice with free boundaries: susceptibility peak and boundary-induced order

On the $\{5,4\}$ hyperbolic lattice, the outermost generation holds 73\% of the sites at all system sizes, making macroscopic averages strictly boundary-dependent. We study the ferromagnetic Ising model on this geometry with free boundaries by Monte Carlo simulation, demonstrating that conventional observables cease to identify a single critical scale. Instead, the finite lattices are organized by two distinct temperature scales. The susceptibility maximum identifies the lower transition scale at $T_{c2}=1.4782(15)J/k_{B}$ without extrapolation. However, the order-parameter distribution lacks a conventional fixed point at this scale. A distinct pseudocritical scale emerges instead at $T^{*}\simeq1.67(3)$ inside the boundary-sensitive intermediate phase, where Binder cumulant curves cross and effective exponents are compatible with mean-field criticality. Between $T_{c2}$ and $T^{*}$, the interior amplifies boundary fluctuations into induced order. Furthermore, because the volume grows exponentially with depth, finite-size scaling must be formulated in the generation index rather than the total number of sites. The lack of asymptotic power-law convergence in the scaling stretch confirms through an independent observable that $T^{*}$ is a finite-size crossover rather than a thermodynamic fixed point. Finally, by applying a coherent field to the outermost generation alone, we recover the upper thermodynamic transition at $T_{pt}=2.81(1)J/k_{B}$, demonstrating that it remains accessible under an appropriate boundary perturbation.

cond-mat.stat-mech↗

arXiv2026

Persistence without Multifractality in Tropical Atlantic SST Indices: Scaling-Range Artefacts and a Reappraisal of the ENSO Association

We investigate the scaling properties of three weekly tropical Atlantic sea-surface-temperature indices (SAT, TSA and the interhemispheric gradient TASI) over 1981--2025 using multifractal detrended fluctuation analysis and its sign-preserving cross-correlation extension. Exponents are estimated over $s\in[18,100]$ weeks, bounded by $s_{\min}\gtrsim6(m+1)$ for second-order detrending and a crossover near 100 weeks. On these scales all three indices are strongly persistent and locally non-stationary ($h(2)=1.32$--$1.35$). Comparison with shuffled and phase-randomised surrogates shows that none of the indices are multifractal within record resolution. SAT ($Δh=0.077$) and TASI ($Δh=0.054$) are fully consistent with both null models. Although TSA yields a larger width ($Δh=0.217$), its increasing $h(q)$ implies the unphysical condition $f(α)>1$, indicating a crossover rather than a multiplicative cascade. At the available record length ($N\approx2300$), apparent multifractal widths are not identifiable because confidence intervals overlap and rankings remain sensitive to analysis choices. The increments are only mildly leptokurtic, excluding heavy tails as the source of the apparent widths. Pairwise couplings reveal strong positive cross-correlations between the regional indices and anticorrelation of the gradient with both, all described by a single cross-scaling exponent, consistent with monofractal behaviour. A lagged analysis further shows that the previously reported TASI--ENSO association disappears after surrogate testing accounting for multiple lags. These results substantially revise downward previous estimates of multifractal strength in tropical Atlantic SST and show that reported widths should not be interpreted without verifying both the sign of $h'(q)$ and the stability of the scaling range.

physics.ao-ph↗

arXiv2026

Multifractal Complexity of the Chandler Wobble and Its Anomalous Disappearance (2015--2020): A MFDFA Study

The Chandler wobble (CW) -- the $\sim$433-day free nutation of Earth's rotation pole -- experienced an anomalous near-disappearance between 2015 and 2020, followed by a re-excitation with an approximately $180^{\circ}$ phase reversal. Using Multifractal Detrended Fluctuation Analysis (MFDFA) applied to more than six decades (1962--2024) of daily IERS EOP C04 polar motion data, this study provides the first multifractal characterisation of the CW and its recent anomaly. Global MFDFA shows that the residual polar motion components and the CW amplitude are genuine multifractal processes with strongly $q$-dependent generalised Hurst exponents and broad singularity spectra. Surrogate-data tests with shuffled and phase-randomised ensembles demonstrate that this multifractality originates from the combined action of long-range temporal correlations and heavy-tailed excitation statistics. A sliding-window analysis reveals a pronounced collapse in long-range persistence and multifractal spectral width of the geometric polar motion signal several years before and during the 2015--2020 amplitude minimum, indicating a genuine dynamical regime change rather than a simple suppression of oscillation amplitude. In contrast, the amplitude- and phase-related variables retain broad multifractal spectra and stable scaling exponents across all epochs, revealing a dynamical decoupling between the geometry of the CW and the multiscale structure of its amplitude and phase fluctuations. These findings highlight the CW amplitude as an exceptionally multifractal integrator of geophysical excitation and suggest that multifractal metrics may provide early-warning indicators of major transitions in Earth rotation dynamics.

cond-mat.stat-mech↗

arXiv2026

MF-toolkit: A High-Performance Python Library for Multifractal Analysis with Automated Crossover Detection, Source Identification and Application to Gravitational Waves Data

Multifractal Detrended Fluctuation Analysis (MFDFA) is a powerful and widely used technique for characterizing the scaling properties and long-range correlations of complex time series. However, its application often involves significant practical challenges, such as the subjective identification of scaling regions (crossovers) and the disambiguation of the physical origins of multifractality. We introduce MF-toolkit, a high-performance, parallelized Python library designed to address these challenges. It integrates three key innovations: (1) fully automatic crossover detection algorithms (CDV-A and SPIC), which remove operator bias and enhance reproducibility; (2) a built-in implementation of the Iterative Amplitude Adjusted Fourier Transform (IAAFT) for generating surrogate data, enabling the robust identification of the source of multifractality; and (3) a comprehensive suite for generating synthetic time series for rigorous validation. We demonstrate the rigor and utility of MF-toolkit through its application to characterize the multifractal properties of non-stationary noise in gravitational wave (LIGO) data. The MF-toolkit library offers a robust, efficient, and user-friendly tool for advanced time series analysis, facilitating more rigorous and reproducible research across physics and other data-intensive fields.

cond-mat.stat-mech↗

arXiv2026

Resolving Spurious Multifractality in Discrete Systems: A Finite-Size Scaling Protocol for MFDFA in the 2D Ising Model

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.

cond-mat.stat-mech↗