Related papers: Order formation processes of complex systems inclu…
We reveal the fractal nature of patterns arising in random sequential adsorption of particles with continuum power-law size distribution, $P(R)\sim R^{\alpha-1}$, $R \le R_{\rm max}$. We find that the patterns become more and more ordered…
The governed equations for the order parameter, one-time and two-time correlators are obtained on the basis of the Langevin equation with the white multiplicative noise which amplitude $x^{a}$ is determined by an exponent $0<a<1$ ($x$ being…
After Boltzmann and Gibbs, the notion of disorder in statistical physics relates to ensembles, not to individual states. This disorder is measured by the logarithm of ensemble volume, the entropy. But recent results about measure…
We study the entropy production rate in systems described by linear Langevin equations, containing mixed even and odd variables under time reversal. Exact formulas are derived for several important quantities in terms only of the means and…
We develop a machine learning algorithm to infer the emergent stochastic equation governing the evolution of an order parameter of a many-body system. We train our neural network to independently learn the directed force acting on the order…
This paper presents a general approach to linear stochastic processes driven by various random noises. Mathematically, such processes are described by linear stochastic differential equations of arbitrary order (the simplest non-trivial…
The confluence of quantum mechanics and complexity, which leads to the emergence of rich, exotic states of matter, motivates the extension of our concepts of quantum ordering. The twin concepts of spontaneously broken symmetry, described in…
Using a notion on the excess entropy of glass with respect to the counterpart crystal, we introduce a simple dimensionless order parameter $\xi$, which changes from $\xi \rightarrow 0$ to $\xi \rightarrow 1$. The former case corresponds to…
Polarization phenomena are essential for the understanding of elementary processes, and are typically large in the threshold region. The selection rules with respect to P-parity, angular momentum, isotopic spin and the Pauli principle allow…
For any translation-invariant quantum lattice system with a symmetry group G, we propose a practical and universal construction of order parameters which identify quantum phase transitions with symmetry-breaking order. They are defined in…
The field of disordered systems provides many simple models in which the competing influences of thermal and non-thermal disorder lead to new phases and non-trivial thermal behavior of order parameters. In this paper, we add a model to the…
In quenched disordered systems, the existence of ordering is generally believed to be only possible in the weak disorder regime (disregarding models of spin-glass type). In particular, sufficiently large random field is expected to prohibit…
We propose a new non-equilibrium model for spatial pattern formation on the basis of local information transfer. Unlike standard models of pattern formation it is not based on the Turing instability. Information is transmitted through the…
We present a numerical study of the order-parameter fluctuations for Ising spin glasses in three and four dimensions at very low temperatures and without an external field. Accurate measurements of two previously introduced parameters, A…
Noise-induced order is the phenomenon by which the chaotic regime of a deterministic system is destroyed in the presence of noise. In this manuscript, we establish noise-induced order for a natural class of systems of dimension $\geq 2$…
We study phase transitions and the nature of order in a class of classical generalized $O(N)$ nonlinear $\sigma$-models (NLS) constructed by minimally coupling pure NLS with additional degrees of freedom in the form of (i) Ising…
Many physical systems are well modeled as collections of interacting particles. Nevertheless, a general approach to quantifying the absolute degree of order immediately surrounding a particle has yet to be described. Motivated thus, we…
A spatially extended classical system with metastable states subject to weak spatiotemporal noise can exhibit a transition in its activation behavior when one or more external parameters are varied. Depending on the potential, the…
In this paper we investigate a quantity called conditional entropy of ordinal patterns, akin to the permutation entropy. The conditional entropy of ordinal patterns describes the average diversity of the ordinal patterns succeeding a given…
We study order-parameter fluctuations (OPF) in disordered systems by considering the behavior of some recently introduced paramaters $G,G_c$ which have proven very useful to locate phase transitions. We prove that both parameters G (for…