Related papers: Growth models on the Bethe lattice
A growing interface subject to noise is described by the Kardar-Parisi-Zhang equation or, equivalently, the noisy Burgers equation. In one dimension this equation is analyzed by means of a weak noise canonical phase space approach applied…
We find a breakdown of the critical dynamic scaling in the coarsening dynamics of an antiferromagnetic {\em XY} model on the kagome lattice when the system is quenched from disordered states into the Kosterlitz-Thouless ({\em KT}) phases at…
There has been much success in describing the limiting spatial fluctuations of growth models in the Kardar-Parisi-Zhang (KPZ) universality class. A proper rescaling of time should introduce a non-trivial temporal dimension to these limiting…
We introduce a set of statistical measures that can be used to quantify non-equilibrium surface growth. They are used to deduce new information about spatiotemporal dynamics of model systems for spinodal decomposition and surface…
Surface growth driven by non-monomeric deposition has remained largely unexplored. We investigate a model based on the deposition of blobs with a power-law size distribution $P(s)\sim s^{-\tau}$. We find that the critical exponents vary…
A nonperturbative weak noise scheme is applied to the Kardar-Parisi-Zhang equation for a growing interface in all dimensions. It is shown that the growth morphology can be interpreted in terms of a dynamically evolving texture of localized…
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…
A series of recent works focused on two-dimensional interface growth models in the so-called Anisotropic KPZ (AKPZ) universality class, that have a large-scale behavior similar to that of the Edwards-Wilkinson equation. In agreement with…
The global effects of sudden changes in the interface growth dynamics are studied using models of the Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) classes during their growth regimes in dimensions $d=1$ and $d=2$. Scaling arguments…
We consider the Kardar-Parisi-Zhang (KPZ) equation for the stochastic growth of an interface of height $h(x,t)$ on the positive half line with boundary condition $\partial_x h(x,t)|_{x=0}=A$. It is equivalent to a continuum directed polymer…
The Kardar-Parisi-Zhang (KPZ) equation has been connected to a large number of important stochastic processes in physics, chemistry and growth phenomena, ranging from classical to quantum physics. The central quest in this field is the…
We study the ballistic deposition and the grain deposition models on two-dimensional substrates. Using the Kardar-Parisi-Zhang (KPZ) ansatz for height fluctuations, we show that the main contribution to the intrinsic width, which causes…
It is known that for the Heisenberg XXZ spin-$\frac{1}{2}$ chain in the critical regime, the scaling limit of the vacuum Bethe roots yields an infinite set of numbers that coincide with the energy spectrum of the quantum mechanical 3D…
Models with a nonequilibrium wetting transition display a transition also in finite systems. This is different from nonequilibrium phase transitions into an absorbing state, where the stationary state is the absorbing one for any value of…
We provide a comprehensive report on scale-invariant fluctuations of growing interfaces in liquid-crystal turbulence, for which we recently found evidence that they belong to the Kardar-Parisi-Zhang (KPZ) universality class for 1+1…
Motivated by an analogy with the spherical model of a ferromagnet, the three Arcetri models are defined. They present new universality classes, either for the growth of interfaces, or else for lattice gases. They are distinct from the…
We study unbinding transitions of a non-equilibrium Kardar-Parisi-Zhang (KPZ) interface in the presence of long-ranged substrates. Both attractive and repulsive substrates, as well as positive and negative Kardar-Parisi-Zhang…
A host of spatially extended systems, both in physics and in other disciplines, are well described at a coarse-grained scale by a Langevin equation with multiplicative-noise. Such systems may exhibit non-equilibrium phase transitions, which…
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…
Stochastic interface dynamics serve as mathematical models for diverse time-dependent physical phenomena: the evolution of boundaries between thermodynamic phases, crystal growth, random deposition... Interesting limits arise at large…