Related papers: Growth models on the Bethe lattice
Statistical behavior and scaling properties of iso-height lines in three different saturated two-dimensional grown surfaces with controversial universality classes are investigated using ideas from Schramm-Loewner evolution (SLE$_\kappa$).…
Depinning of elastic systems advancing on disordered media can usually be described by the quenched Edwards-Wilkinson equation (qEW). However, additional ingredients such as anharmonicity and forces that can not be derived from a potential…
Control of generically scale-invariant systems, i.e., targeting specific cooperative features in non-linear stochastic interacting systems with many degrees of freedom subject to strong fluctuations and correlations that are characterized…
We investigate the origin of the scaling corrections in ballistic deposition models in high dimensions using the method proposed by Alves \textit{et al}. [Phys Rev. E \textbf{90}, 052405 (20014)] in $d=2+1$ dimensions, where the intrinsic…
We discuss the features of nonequilibrium growth problems, their scaling description and their differences from equilibrium problems. The emphasis is on the Kardar-Parisi-Zhang equation and the renormalization group point of view. Some of…
We investigate numerically the effects of long-range temporal and spatial correlations based on the rescaled distributions of the squared interface width $W^2(L,t)$ and the interface height $h(x,t)$ in the (1+1)-dimensional…
We consider the coagulation-decoagulation model on an one-dimensional lattice of length $L$ with open boundary conditions. Based on the empty interval approach the time evolution is described by a system of $\frac{L(L+1)}{2}$ differential…
We discuss relaxation and aging processes in the one- and two-dimensional $ABC$ models. In these driven diffusive systems of three particle types, biased exchanges in one direction yield a coarsening process characterized in the long time…
We discuss space-time chaos and scaling properties for classical non-Abelian gauge fields discretized on a spatial lattice. We emphasize that there is a ``no go'' for simulating the original continuum classical gauge fields over a long time…
We study the Bethe approximation for a system of long rigid rods of fixed length k, with only excluded volume interaction. For large enough k, this system undergoes an isotropic-nematic phase transition as a function of density of the rods.…
The Kardar-Parisi-Zhang (KPZ) equation is a celebrated non-linear stochastic equation featuring non-equilibrium scaling. Although in one dimension, its statistical properties are very well understood, a new scaling regime has been reported…
We obtain several exact results for universal distributions involving the maximum of the Airy$_2$ process minus a parabola and plus a Brownian motion, with applications to the 1D Kardar-Parisi-Zhang (KPZ) stochastic growth universality…
We study height and roughness distributions of films grown with discrete Kardar-Parisi-Zhang (KPZ) models in a small time regime which is expected to parallel the typical experimental conditions. Those distributions are measured with square…
In this work, the out-of-equilibrium dynamics of the Kardar-Parisi-Zhang equation in (1+1) dimensions is studied by means of numerical simulations, focussing on the two-times evolution of an interface in the absence of any disordered…
The effects of a randomly moving environment on a randomly growing interface are studied by the field theoretic renormalization group analysis. The kinetic growth of an interface (kinetic roughening) is described by the Kardar-Parisi-Zhang…
We studied the non-equilibrium dynamics of the q-state Potts model in the square lattice, after a quench to sub-critical temperatures. By means of a continuous time Monte Carlo algorithm (non-conserved order parameter dynamics) we analyzed…
At the beginning of the 70's, Baxter introduced a multiparametric generalization of the six-vertex model. This integrable system has been found to exhibit a remarkable variety of critical behaviors. The work is part of a series of papers…
The Kardar-Parisi-Zhang universality class of stochastic surface growth is studied by exact field-theoretic methods. From previous numerical results, a few qualitative assumptions are inferred. In particular, height correlations should…
We study an anisotropic variant of the two-dimensional Kardar-Parisi-Zhang equation, that is relevant to describe growth of vicinal surfaces and has Gaussian, logarithmically rough, stationary states. While the folklore belief (based on…
We reexamine the range of validity of finite-size scaling in the $\phi^4$ lattice model and the $\phi^4$ field theory below four dimensions. We show that general renormalization-group arguments based on the renormalizability of the $\phi^4$…