Related papers: Finite-time scaling for kinetic rough interfaces
We present a simple one dimensional stochastic model with three control parameters and a surprisingly rich zoo of phase transitions. At each (discrete) site $x$ and time $t$, an integer $n(x,t)$ satisfies a linear interface equation with…
We investigate a two-dimensional Ising model with long-range interactions that emerge from a generalization of the magnetic dipolar interaction in spin systems with in-plane spin orientation. This interaction is, in general, anisotropic…
Single-time and two-time correlators are computed exactly in the $1D$ Glauber-Ising model after a quench to zero temperature and on a periodic chain of finite length $N$, using a simple analytical continuation technique. Besides the general…
In the last few years, the methods of constructive Fermionic Renormalization Group have been successfully applied to the study of the scaling limit of several two-dimensional statistical mechanics models at the critical point, including:…
A wide range of non-equilibrium phenomena in nature involve non-reciprocal interactions. To understand the novel behaviors that can emerge in such systems, finding tractable models is essential. With this goal, we introduce a non-reciprocal…
Conserved surface roughening represents a special case of interface dynamics where the total height of the interface is conserved. Recently, it was suggested [F. Caballero et al., Phys. Rev. Lett. 121, 020601 (2018)] that the original…
We have investigated the dynamics of domain walls in the cubic anisotropy model. In this model a global O(N) symmetry is broken to a set of discrete vacua either on the faces, or vertices of a (hyper)cube. We compute the scaling exponents…
We study the roughening of interfaces in phase-separated active suspensions on substrates. At both large length and timescales, we show that the interfacial dynamics belongs to the |q|KPZ universality class discussed in Besse et al. Phys.…
A model in which a three-dimensional elastic medium is represented by a network of identical masses connected by springs of random strengths and allowed to vibrate only along a selected axis of the reference frame, exhibits an Anderson…
We investigate solid-on-solid models that belong to the Kardar-Parisi-Zhang (KPZ) universality class on substrates that expand laterally at a constant rate by duplication of columns. Despite the null global curvature, we show that all…
In discrete models describing growing rough interfaces of the Kardar-Parisi-Zhang universality class, we examine height fluctuations at a fixed site as a function of time in the monolayer unit. For small systems, we show that it is possible…
We provide a detailed Dynamic Renormalization Group study for a class of stochastic equations that describe non-conserved interface growth mediated by non-local interactions. We consider explicitly both the morphologically stable case, and…
We study the dynamic scaling hypothesis in invariant surface growth. We show that the existence of power-law scaling of the correlation functions (scale invariance) does not determine a unique dynamic scaling form of the correlation…
Self-affine rough interfaces are ubiquitous in experimental systems, and display characteristic scaling properties as a signature of the nature of disorder in their supporting medium, i.e. of the statistical features of its heterogeneities.…
We propose a simple discrete model to study the nonequilibrium fluctuations of two locally coupled 1+1 dimensional systems (interfaces). Measuring numerically the tilt-dependent velocity we construct a set of stochastic continuum equations…
Using stability arguments, this Brief Report suggests that a term that enhances the surface tension in the presence of large height fluctuations should be included in the Kardar-Parisi-Zhang equation. A one-loop renormalization group…
In this paper, we develop a scaled gradient-momentum framework for continuous-time optimization that achieves global finite-time convergence. A state-dependent scaling mechanism is introduced to enable classical dynamics, such as…
Recent work has introduced the concept of finite-time scaling to characterize bifurcation diagrams at finite times in deterministic discrete dynamical systems, drawing an analogy with finite-size scaling used to study critical behavior in…
Height fluctuations of growing surfaces can be characterized by the probability distribution of height in a spatial point at a finite time. Recently there has been spectacular progress in the studies of this quantity for the…
Scaling of the mean velocity profiles has been studied by many researchers, since it provides a template of universal dynamical patterns across a range of Reynolds numbers. Various normalization schemes have been shown in the past, some…