相关论文: On the existence of an upper critical dimension fo…
Simulations of restricted solid-on-solid growth models are used to build the width-distributions of d=2-5 dimensional KPZ interfaces. We find that the universal scaling function associated with the steady-state width-distribution changes…
Numerical results for the Directed Polymer model in 1+4 dimensions in various types of disorder are presented. The results are obtained for system size considerably larger than that considered previously. For the extreme strong disorder…
The upper critical dimension of the Ising model is known to be $d_c=4$, above which critical behavior is regarded as trivial. We hereby argue from extensive simulations that, in the random-cluster representation, the Ising model…
We study the mode-coupling approximation for the KPZ equation in the strong coupling regime. By constructing an ansatz consistent with the asymptotic forms of the correlation and response functions we determine the upper critical dimension…
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…
The controversy whether or not he Kardar-Parisi-Zhang (KPZ) equation has an upper critical dimension (UCD) is going on for quite a long time. Some approximate integral equations for the two-point function served as an indication for the…
We study the KPZ equation (in D = 2, 3 and 4 spatial dimensions) by using a RSOS discretization of the surface. We measure the critical exponents very precisely, and we show that the rational guess is not appropriate, and that 4D is not the…
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…
In this work we generalize the etching model (Mello et al 2001 Phys. Rev. E 63 041113) to d + 1 dimensions. The dynamic exponents of this model are compatible with those of the Kardar-Parisi-Zhang universality class. We investigate the…
The strong-coupling regime of Kardar-Parisi-Zhang surface growth driven by short-ranged noise has an upper critical dimension d_> less or equal to four (where the dynamic exponent z takes the value z (d_>) = 2). To derive this, we use the…
We show that the theoretical machinery developed for the Kardar-Parisi-Zhang (KPZ) class in low dimensions are obeyed by the restricted solid-on-solid (RSOS) model for substrates with dimensions up to $d=6$. Analyzing different restriction…
Aiming to investigate the upper critical dimension, $d_u$, of the KPZ class, in [EPL 103 (2013) 10005] some growth models were numerically analyzed using Cayley trees (CTs) as substrates, as a way to access their behavior in the…
The pinning-depinning phase transitions of interfaces for two classes of discrete elastic-string models are investigated numerically. In the (1+1)-dimensions, we revisit these two elastic-string models with slight modification to growth…
The dynamical regimes of models belonging to the Kardar-Parisi-Zhang (KPZ) universality class are investigated in d=2+1 by extensive simulations considering flat and curved geometries. Geometry-dependent universal distributions, different…
We assess the dependence on substrate dimensionality of the asymptotic scaling behavior of a whole family of equations that feature the basic symmetries of the Kardar-Parisi-Zhang (KPZ) equation. Even for cases in which, as expected from…
In this work we analyze the universal scaling functions and the critical exponents at the upper critical dimension of a continuous phase transition. The consideration of the universal scaling behavior yields a decisive check of the value of…
We derive the exact actions of the $Q$-state Potts model valid on any graph, first for the spin degrees of freedom, and second for the Fortuin-Kasteleyn clusters. In both cases the field is a traceless $Q$-component scalar field…
Numerical investigation of critical exponents on a hypercubic with L^d random sites with L up to $33 and d up to 7 show that above the critical dimension the phase transitions in Ising model and percolation are not alike.
We present a unifying, consistent, finite-size-scaling picture for percolation theory bringing it into the framework of a general, renormalization-group-based, scaling scheme for systems above their upper critical dimensions $d_c$.…
Recently, we argued [Chin. Phys. Lett. $39$, 080502 (2022)] that the Ising model simultaneously exhibits two upper critical dimensions $(d_c=4, d_p=6)$ in the Fortuin-Kasteleyn (FK) random-cluster representation. In this paper, we perform a…