arXiv subjects

J. M. Marcos

Publications and source records attributed to J. M. Marcos.

6 recordsLinked to original sources

arXiv2026

On the upper critical dimension of the KPZ universality class: KPZ and related equations on a fully connected graph

We investigate the infinite-dimensional limit of nonequilibrium surface growth by numerically integrating stochastic growth equations on a fully connected graph. In particular, we study the Edwards-Wilkinson (EW), Kardar-Parisi-Zhang (KPZ), and tensionless KPZ (TKPZ) equations. Using a network discretization adapted to the all-to-all interaction topology, we analyze the global roughness, height-fluctuation statistics, time power spectra, and two-time correlations. For the EW equation, we obtain an exact expression for the roughness that matches the numerical simulations and shows that the interface becomes flat as the number of nodes in the graph, $N$, tends to infinity. We also compute analytically the time power spectrum, show that height fluctuations are Gaussian, and derive an explicit expression for the two-time height autocorrelation function, indicating that the aging behavior is trivial. For the KPZ equation, finite-size and strong-coupling effects can cause deviations from EW behavior at moderate system sizes $N$, often accompanied by numerical instabilities; however, these differences disappear as $N$ increases. In the large-$N$ limit, KPZ dynamics converges to EW behavior, as the four observables analyzed exhibit identical scaling properties. Overall, our results indicate that on a fully connected graph the KPZ nonlinearity is irrelevant as $N\to\infty$, leading to EW-like dynamics with asymptotically flat interfaces. These findings are interpreted in the context of the upper critical dimension of the KPZ universality class.

cond-mat.stat-mech↗

arXiv2026

Discrete Lattice Models for Interface Growth on a Complete Graph

We investigate the behavior of discrete interface growth models belonging to the Edwards--Wilkinson (EW) and Kardar--Parisi--Zhang (KPZ) universality classes, when defined on a complete graph, a topology commonly used to probe the infinite-dimensional limit of statistical mechanical systems. Our aim is to assess to what extent discrete lattice models reproduce the behavior of their corresponding continuum equations in this highly connected setting. After assessing the trivial behavior shown by some well known cases (like random deposition with surface relaxation or the etching model), we focus on two paradigmatic models associated with the KPZ universality class, the Restricted Solid-on-Solid (RSOS) and Ballistic Deposition (BD) models, and assess non-trivial behavior through several observables including the roughness, height fluctuations, power spectra, and two-time autocorrelation functions. Still, despite similarities with continuum equations, important differences arise in the fluctuations and long-time dynamics. In both discrete models the rescaled height fluctuations display a pronounced left tail, indicating the presence of lagging nodes. While the RSOS model exhibits a saturation roughness that decreases with system size, similarly to the EW and KPZ equations, the BD model exhibits a saturation roughness that increases with system size and an additional ultrafast growth regime, placing it outside the KPZ universality class on a complete graph.

cond-mat.stat-mech↗

arXiv2025

Spreading fronts: numerical simulations on discrete models and continuous equations

Out-of-equilibrium systems, inherently complex and challenging to understand, are prevalent across various disciplines, including physics where they arise in contexts such as fluid dynamics. In particular, critical out-of-equilibrium systems combine this complexity with the scaling laws and universality classes observed in critical phenomena, with kinetic surface roughening, the study of how a flat surface becomes progressively rougher over time, serving as a prime example. This behavior manifests in a wide variety of contexts, including metal corrosion, cell proliferation, and, notably, the growth of thin films, which can emerge as a result of wetting processes. In this thesis, we conduct extensive numerical simulations to study critical fluctuations and identify universal features of several rough interfaces, generated by simulating discrete models of thin film growth and by performing direct numerical integration of continuum equations. To explore the universal behavior of these interfaces, we identify the critical exponents that characterize the spatio-temporal fluctuations of the front. Additionally, we analyze the dynamics of thin films across different physical scenarios to deepen our understanding of their behavior in out-of-equilibrium conditions, especially in the case where these films are formed by the action of an external force such as Surface Acoustic Waves.

cond-mat.stat-mech↗

arXiv2025

Numerical Integration of the KPZ and Related Equations on Networks: The Case of the Cayley Tree

The numerical integration of stochastic growth equations on non-Euclidean networks presents unique challenges due to the nonlinearities that occur in many relevant models and of the structural constraints of the networks. In this work, we integrate the KPZ, Edwards-Wilkinson, and tensionless KPZ equations on Cayley trees using different numerical schemes and compare their behavior with previous results obtained for discrete growth models. By assessing the stability and accuracy of these methods, we explore how network topology influences interface growth and how boundary effects shape the observed scaling properties. Our results show good agreement with previous studies on discrete models, reinforcing key scaling behaviors while highlighting some differences. These findings contribute to a better understanding of surface growth on networked substrates and provide a computational framework for studying nonlinear stochastic processes beyond Euclidean lattices.

cond-mat.stat-mech↗

arXiv2025

Microscopic fluctuations in the spreading fronts of circular wetting liquid droplets

We study numerically the kinetic roughening properties of the precursor fronts of nonvolatile liquid droplets spreading on solid substrates, for the case of circular droplets, more frequently addressed in experiments. To this end, we perform kinetic Monte Carlo (kMC) simulations of a lattice gas model whose kinetic roughening behavior has been recently assessed in a band geometry [J.\ M.\ Marcos {\em et al.}, Phys.\ Rev.\ E {\bf 105}, 054801 (2022)]. We compare the scaling behaviors of the spreading fronts obtained for the two geometries, in view of the occurrence of, for example, different universality subclasses for different growth geometries for the related important Kardar-Parisi-Zhang (KPZ) universality class. For circular droplets we obtain that the average front position increases (sub-)diffusively as $R\sim t^δ$, where $δ\lesssim 1/2$ shows a stronger dependence on the conditions considered for temperature and substrate wettability than in band geometry. In spite of this, front fluctuations for circular droplets behave qualitatively similar to those seen for band geometries, with kinetic roughening exponent values which similarly depend on temperature $T$ but become $T$-independent for sufficiently high $T$. Circular droplets also display intrinsic anomalous scaling with different values of the roughness exponent at short and large length scales, and fluctuations statistics which are close to the Tracy-Widom probability distribution function that applies in the corresponding KPZ universality subclass, now the one expected for interfaces with an overall circular symmetry.

cond-mat.stat-mech↗

arXiv2022

Spreading fronts of wetting liquid droplets: microscopic simulations and universal fluctuations

We have used kinetic Monte Carlo (kMC) simulations of a lattice gas to study front fluctuations in the spreading of a non-volatile liquid droplet onto a solid substrate. Our results are consistent with a diffusive growth law for the radius of the precursor layer, $R \sim t^δ$, with $δ\approx 1/2$ in all the conditions considered for temperature and substrate wettability, in good agreement with previous studies. The fluctuations of the front exhibit kinetic roughening properties with exponent values which depend on temperature $T$, but become $T$-independent for sufficiently high $T$. Moreover, strong evidences of intrinsic anomalous scaling have been found, characterized by different values of the roughness exponent at short and large length scales. Although such a behavior differs from the scaling properties of the one-dimensional Kardar-Parisi-Zhang (KPZ) universality class, the front covariance and the probability distribution function of front fluctuations found in our kMC simulations do display KPZ behavior, agreeing with simulations of a continuum height equation proposed in this context. However, this equation does not feature intrinsic anomalous scaling, at variance with the discrete model.

cond-mat.stat-mech↗