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We demonstrate the non-universal behavior of finite size scaling in (1+1) dimension of a nonlinear discrete growth model involving extended particles in generalized point of view. In particular, we show the violation of the universal nature…
One of the most impressive features of continuous phase transitions is the concept of universality, that allows to group the great variety of different critical phenomena into a small number of universality classes. All systems belonging to…
Recently, the concept of geometric renormalization group provides a good approach for studying the structural symmetry and functional invariance of complex networks. Along this line, we systematically investigate the finite-size scaling of…
Two-dimensional directed site percolation is studied in systems directed along the x-axis and limited by a free surface at y=\pm Cx^k. Scaling considerations show that the surface is a relevant perturbation to the local critical behaviour…
Physical kinetic roughening processes are well known to exhibit universal scaling of observables that fluctuate in space and time. Are there analogous dynamic scaling laws that are unique to the chemical reaction mechanisms available…
Finite-size scaling (FSS) for a critical phase transition ($t=0$) states that within a window of size $|t|\sim L^{-1/\nu}$, the scaling behavior of any observable $Q$ in a system of linear size $L$ asymptotically follows a scaling form as…
In systems of diffusing particles, we investigate large deviations of a time-averaged measure of clustering around one particle. We focus on biased ensembles of trajectories, which realise large-deviation events. The bias acts on a single…
Airplane boarding process is an example where disorder properties of the system are relevant to the emergence of universality classes. Based on a simple model, we present a systematic analysis of finite-size effects in boarding time, and…
We present a pedagogical review of the universal scaling properties displayed by the structure function F_2 at small x and large Q^2 as measured at HERA. We first describe the derivation of the double asymptotic scaling of F_2 from the…
Order parameter fluctuations for the two dimensional Ising model in the region of the critical temperature are presented. A locus of temperatures T*(L) and of magnetic fields B*(L) are identified, for which the probability density function…
Force networks form the skeleton of static granular matter. They are the key ingredient to mechanical properties, such as stability, elasticity and sound transmission, which are of utmost importance for civil engineering and industrial…
Finite-size scaling is a key tool in statistical physics, used to infer critical behavior in finite systems. Here we use the analogous concept of finite-time scaling to describe the bifurcation diagram at finite times in discrete dynamical…
The influence of the initial fluctuations on the onset of scaling in the quench to zero temperature of a two dimensional system with conserved order parameter, is analyzed in detail with and without topological defects. We find that the…
Dynamical universality plays a fundamental role in understanding the scaling properties of critical dynamics, including absorbing phase transitions and physical aging. Although individual universality classes have been extensively studied,…
It is proposed that the $O(n)$ spin and geometrical percolation models can help to study the QCD phase diagram due to the universality properties of the phase transition. In this paper, correlations and fluctuations of various sizes of…
Scale invariance and the resulting power law behaviours are seen in diverse systems. In this work we consider translation, rotational and scale invariant systems defined on a lattice, such that the variables defining the state at every…
The onset of rigidity in interacting liquids, as they undergo a transition to a disordered solid, is associated with a rearrangement of the low-frequency vibrational spectrum. In this letter, we derive scaling forms for the singular…
We show by extensive simulations that the whole supercritical phase of the three-dimensional uniform forest model simultaneously exhibits an infinite tree and a rich variety of critical phenomena. Besides typical scalings like algebraically…
This is a brief survey of recent experimental studies on out-of-equilibrium scaling laws, focusing on two prominent situations where non-trivial universality classes have been identified theoretically: absorbing-state phase transitions and…
We introduce a correlated static model and investigate a percolation transition. The model is a modification of the static model and is characterized by assortative degree-degree correlation. As one varies the edge density, the network…