Related papers: Finite-time scaling in local bifurcations
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…
Estimating a fractal dimension from a finite stochastic trajectory is a finite-size scaling problem: the apparent box-counting exponent is shaped by an occupancy crossover between the resolved range of scales and the finite number of…
Single-time and two-time correlators are computed exactly in the $1D$ Glauber-Ising model after a quench to zero temperature and on a periodic chain of finite length $N$, using a simple analytical continuation technique. Besides the general…
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…
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 investigate scaling phenomena at first-order quantum transitions, when the boundary conditions favor one of the two phases. We show that the corresponding finite-size scaling behavior, arising from the interplay between the driving…
We study a discrete non-autonomous system whose autonomous counterpart (with the frozen bifurcation parameter) admits a saddle-node bifurcation, and in which the bifurcation parameter slowly changes in time and is characterized by a sweep…
This paper presents an in-depth analysis of the anatomy of both thermodynamics and statistical mechanics, together with the relationships between their constituent parts. Based on this analysis, using the renormalization group and…
Results for transport properties, in conjunction with phase behavior and thermodynamics, are presented at the criticality of a binary Lennard-Jones fluid from Monte Carlo and molecular dynamics simulations. Evidence for much stronger…
Universality, where microscopic details become irrelevant, takes place in thermodynamic phase transitions. The universality is captured by a singular scaling function of the thermodynamic variables, where the scaling exponents are…
We propose a unified scaling theory of entanglement entropy in the confinements of finite bond dimensions, dynamics and system sizes. Within the theory, the finite-entanglement scaling introduced recently is generalized to the dynamics…
We investigate finite-size effects on the chiral phase diagram of strong interactions within the linear sigma model coupled to quarks. We estimate the modification of the pseudocritical transition line and isentropic trajectories for sizes…
To study the kinetics of phase separation in active matter systems, we consider models that impose a Vicsek-type self-propulsion rule on otherwise passive particles interacting via the Lennard-Jones potential. Two types of kinetics are of…
We demonstrate that scale-free patterns are observed in a spatially extended stochastic system whose deterministic part undergoes a saddle-node bifurcation. Remarkably, the scale-free patterns appear only at a particular time in relaxation…
We study the finite-size scaling behaviour at the critical point, resulting from the addition of a homogeneous size-dependent perturbation, decaying as an inverse power of the system size. The scaling theory is first formulated in a general…
The interest in the topological properties of materials brings into question the problem of topological phase transitions. As a control parameter is varied, one may drive a system through phases with different topological properties. What…
We investigate finite size scaling in percolating widthless stick systems with variable aspect ratios in an extensive Monte Carlo simulation study. A generalized scaling function is introduced to describe the scaling behavior of the…
By solving the Schr\"odinger equation one obtains the whole energy spectrum, both the bound and the continuum states. If the Hamiltonian depends on a set of parameters, these could be tuned to a transition from bound to continuum states.…
Accepting validity of self-consistent theory of localization by Vollhardt and Woelfle, we derive the finite-size scaling procedure used for studies of the critical behavior in d-dimensional case and based on the use of auxiliary quasi-1D…
This chapter describes the progress made during the past three decades in the finite size scaling analysis of the critical phenomena of the Anderson transition. The scaling theory of localisation and the Anderson model of localisation are…