Related papers: Finite-time scaling in local bifurcations
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…
Finite-size effects in systems with diverging characteristic lengthscale have been addressed via state-of-the-art Monte Carlo and molecular dynamics simulations of various models exhibiting solid-solid, liquid-liquid and vapor-liquid…
It is pointed out that finite-size effect is not negligible in locating critical point of QCD phase transition at current relativistic heavy ion collisions. Finite-size behavior near critical point, in particular, finite-size scaling and…
We analyze situations where a saddle-node bifurcation occurs on a fractal basin boundary. Specifically, we are interested in what happens when a system parameter is slowly swept in time through the bifurcation. Such situations are known to…
To understand the finite-size-scaling properties of phases transitions in classical and quantum models in the presence of quenched disorder, it has proven to be fruitful to introduce the notion of a finite-size-pseudo-critical point in each…
The critical point of a topological phase transition is described by a conformal field theory, where finite-size corrections to energy are uniquely related to its central charge. We investigate the finite-size scaling away from criticality…
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…
In the 1960's, four famous scaling relations were developed which relate the six standard critical exponents describing continuous phase transitions in the thermodynamic limit of statistical physics models. They are well understood at a…
Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful conceptual and mathematical tools were…
Phenomenological scaling arguments suggest the existence of universal amplitudes in the finite-size scaling of certain correlation lengths in strongly anisotropic or dynamical phase transitions. For equilibrium systems, provided that…
Near a bifurcation point a system experiences critical slowing down. This leads to scaling behavior of fluctuations. We find that a periodically driven system may display three scaling regimes and scaling crossovers near a saddle-node…
Finite-size scaling at fixed renormalization-group invariant is a powerful and flexible technique to analyze Monte Carlo data at a critical point. It consists in fixing a given renormalization-group invariant quantity to a given value,…
The finite-size scaling (FSS) theory for continuous phase transitions has been useful in determining the critical behavior from the size dependent behaviors of thermodynamic quantities. When the phase transition is discontinuous, however,…
Fluctuations of thermodynamic quantities become non-negligible and play an important role when the system size is small. We develop finite-time thermodynamics of fluctuations in microscopic heat engines whose environmental temperature and…
We investigate the dynamic behavior of finite-size systems close to a first-order transition (FOT). We develop a dynamic finite-size scaling (DFSS) theory for the dynamic behavior in the coexistence region where different phases coexist. It…
Critical transitions (or tipping points) are drastic sudden changes observed in many dynamical systems. Large classes of critical transitions are associated to systems, which drift slowly towards a bifurcation point. In the context of…
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…
We study systems with a continuous phase transition that tune their parameters to maximize a quantity that diverges solely at a unique critical point. Varying the size of these systems with dynamically adjusting parameters, the same…
The fluctuation scaling law has universally been observed in a wide variety of phenomena. For counting processes describing the number of events occurred during time intervals, it is expressed as a power function relationship between the…
Slowing down phenomena occur in both deterministic and stochastic dynamical systems at the vicinity of phase transitions or bifurcations. An example is found in systems exhibiting a saddle-node bifurcation, which undergo a dramatic time…