Related papers: On the Finite Size Scaling in Disordered Systems
We test the universal finite-size scaling of the cluster mass order parameter in two-dimensional (2D) isotropic and directed continuum percolation models below the percolation threshold by computer simulations. We found that the simulation…
A finite size scaling theory for the partition function zeros and thermodynamic functions of O(N) phi^4-theory in four dimensions is derived from renormalization group methods. The leading scaling behaviour is mean-field like with…
We analyze the finite size corrections to entanglement in quantum critical systems. By using conformal symmetry and density functional theory, we discuss the structure of the finite size contributions to a general measure of ground state…
Collective behaviour in biological systems is often accompanied by strong correlations. The question has therefore arisen of whether correlation is amplified by the vicinity to some critical point in the parameters space. Biological…
A binary liquid near its consolute point exhibits critical fluctuations of the local composition; the diverging correlation length has always challenged simulations. The method of choice for the calculation of critical points in the phase…
Exact results of the finite-size behavior of the susceptibility in three-dimensional mean spherical model films under Dirichlet-Dirichlet, Dirichlet-Neumann and Neumann-Neumann boundary conditions are presented. The corresponding scaling…
The behaviour of a d-dimensional vectorial N=3 model at a m-axial Lifshitz critical point is investigated by means of a nonperturbative renormalization group approach that is free of the huge technical difficulties that plague the…
Dynamical scaling and ageing in disordered systems far from equilibrium is reviewed. Particular attention is devoted to the question to what extent a recently introduced generalization of dynamical scaling to local scale-invariance can…
The onset of synchronization in a system of random frequency oscillators coupled through a random network is investigated. Using a mean-field approximation, we characterize sample-to-sample fluctuations for networks of finite size, and…
There has been a long running debate on the finite size scaling for the Ising model with free boundary conditions above the upper critical dimension, where the standard picture gives a $L^2$ scaling for the susceptibility and an alternative…
A d-dimensional finite quantum model system confined to a general hypercubical geometry with linear spatial size L and ``temporal size'' 1/T (T - temperature of the system) is considered in the spherical approximation under periodic…
Pinning models are built from discrete renewal sequences by rewarding (or penalizing) the trajectories according to their number of renewal epochs up to time $N$, and $N$ is then sent to infinity. They are statistical mechanics models to…
The scaling form of the whole distribution P(D) of the random diffusion coefficient D(x) in a model of classically diffusing particles is investigated. The renormalization group approach above the lower critical dimension d=0 is applied to…
The scaling of correlations as a function of system size provides important hints to understand critical phenomena on a variety of systems. Its study in biological systems offers two challenges: usually they are not of infinite size, and in…
We propose a finite-size scaling analysis of binary stochastic processes $X(t)\in \{0,1\}$ based on the second moment correlation length $\xi$ for the autocorrelation function $C(t)$. The purpose is to clarify the critical properties and…
Numerical studies of the domain chaos state in a model of rotating Rayleigh-Benard convection suggest that finite size effects may account for the discrepancy between experimentally measured values of the correlation length and the…
We analyze numerically three different models exhibiting an absorbing phase transition. We focus on the finite-size scaling as well as the dynamical scaling behavior. An accurate determination of several critical exponents allows to…
Using the $x-y$ model and a non-local updating scheme called cluster Monte Carlo, we calculate the superfluid density of a two dimensional superfluid on large-size square lattices $L \times L$ up to $400\times 400$. This technique allows us…
We study the surface critical behavior of semi-infinite systems belonging to the bulk universality class of the Ising model. Special attention is paid to the local behavior of experimentally relevant quantities such as the order parameter…
We study two models having an infinite-disorder critical point --- the zero temperature random transverse-field Ising model and the random contact process --- on a star-like network composed of $M$ semi-infinite chains connected to a common…