Related papers: Bifurcation and Criticality
We study numerically the non-equilibrium critical properties of the Ising model defined on direct products of graphs, obtained from factor graphs without phase transition (Tc = 0). On this class of product graphs, the Ising model features a…
A system driven in the vicinity of its critical point by varying a relevant field in an arbitrary function of time is a generic system that possesses a long relaxation time compared with the driving time scale and thus represents a large…
The classical pitchfork of singularity theory is a twice-degenerate bifurcation that typically occurs in dynamical system models exhibiting Z_2 symmetry. Non-classical pitchfork singularities also occur in many non-symmetric systems, where…
We examine the Jarzynski equality for a quenching process across the critical point of second-order phase transitions, where absolute irreversibility and the effect of finite-sampling of the initial equilibrium distribution arise on an…
Nonequilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and Kawasaki-type spin-exchange kinetics at infinite temperature T are investigated here in one dimension from the point of view of…
The theory of continuous phase transitions predicts the universal collective properties of a physical system near a critical point, which for instance manifest in characteristic power-law behaviours of physical observables. The…
A rigorous mathematical framework for analyzing the chemical master equation (CME) with bistability, based on the theory of large deviation, is proposed. Using a simple phosphorylation-dephosphorylation cycle with feedback as an example, we…
We present two classes of nonequilibrium models with critical behavior. Each model is characterized by an integer $q>1$, and is defined on configurations of $q$-valued spins on regular lattices. The definitions of the models are very…
We study the critical behavior and the out-of-equilibrium dynamics of a two-dimensional Ising model with non-static interactions. In our model, bonds are dynamically changing according to a majority rule depending on the set of closest…
We revisit a recent claim that the Earth's climate system is characterized by sensitive dependence to parameters; in particular, that the system exhibits an asymmetric, large-amplitude response to normally distributed feedback forcing. Such…
Non-equilibrium critical phenomena generally exist in many dynamic systems, like chemical reactions and some driven-dissipative {reactive} particle systems. Here, by using computer simulation and theoretical analysis, we demonstrate the…
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…
Many-variable differential equations with random coefficients provide powerful models for the dynamics of many interacting species in ecology. These models are known to exhibit a dynamical phase transition from a phase where population…
We study the nonequilibrium critical point of the zero temperature random field Ising model on a triangular lattice and compare it with known results on honeycomb, square, and simple cubic lattices. We suggest that the coordination number…
We analyzed the entropy production in the majority-vote model by using a mean-field approximation and Monte Carlo simulations. The dynamical rules of the model do not obey detailed balance so that entropy is continuously being produced.…
Determining critical points of phase transitions from partial data is essential to avoid abrupt system collapses and reducing experimental or computational costs. However, the complex physical systems and phase transition phenomena have…
Stochastic thermodynamics gives universal relations for microscopic entropy production, yet its critical behavior at macroscopic nonequilibrium transitions remains unclassified. We study well-mixed reversible chemical reaction networks in…
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…
We analyze critical points that can be induced in glassy systems by the presence of constraints. These critical points are predicted by the Mean Field Thermodynamic approach and they are precursors of the standard glass transition in…
Nonlinear dynamical systems may be exposed to tipping points, critical thresholds at which small changes in the external inputs or in the systems parameters abruptly shift the system to an alternative state with a contrasting dynamical…