Nonequilibrium Critical Dynamics Research Articles

Nonequilibrium critical dynamics of the two-dimensional ±J Ising model.

The ±J Ising model is a simple frustrated spin model, where the exchange couplings independently take the discrete value -J with probability p and +J with probability 1-p. It is especially appealing due to its connection to quantum error correcting codes. Here, we investigate the nonequilibrium critical behavior of the two-dimensional ±J Ising model, after a quench from different initial conditions to a critical point T_{c}(p) on the paramagnetic-ferromagnetic (PF) transition line, especially above, below, and at the multicritical Nishimori point (NP). The dynamical critical exponent z_{c} seems to exhibit nonuniversal behavior for quenches above and below the NP, which is identified as a preasymptotic feature due to the repulsive fixed point at the NP, whereas for a quench directly to the NP, the dynamics reaches the asymptotic regime with z_{c}≃6.02(6). We also consider the geometrical spin clusters (of like spin signs) during the critical dynamics. Each universality class on the PF line is uniquely characterized by the stochastic Loewner evolution with corresponding parameter κ. Moreover, for the critical quenches from the paramagnetic phase, the model, irrespective of the frustration, exhibits an emergent critical percolation topology at the large length scales.

Nonequilibrium critical dynamics of the ferromagnetic Ising chain subject to slow cooling: Kawasaki’s spin-exchange kinetics

Nonequilibrium critical dynamics of the ferromagnetic Ising chain subject to slow cooling: Kawasaki’s spin-exchange kinetics

Nonequilibrium critical dynamics of two dimensional Ising model under slow cooling and heating

Nonequilibrium critical dynamics of two dimensional Ising model under slow cooling and heating

Critical dynamics of anisotropic antiferromagnets in an external field.

We numerically investigate the nonequilibrium critical dynamics in three-dimensional anisotropic antiferromagnets in the presence of an external magnetic field. The phase diagram of this system exhibits two critical lines that meet at a bicritical point. The nonconserved components of the staggered magnetization order parameter couple dynamically to the conserved component of the magnetization density along the direction of the external field. Employing a hybrid computational algorithm that combines reversible spin precession with relaxational Monte Carlo updates, we study the aging scaling dynamics for the model C critical line, identifying the critical initial slip, autocorrelation, and aging exponents for both the order parameter and the conserved field, thus also verifying the dynamic critical exponent. We further probe the model F critical line by investigating the system size dependence of the characteristic spin wave frequencies near criticality and measure the dynamic critical exponents for the order parameter including its aging scaling at the bicritical point.

Marginal Effect of Structural Defects on the Nonequilibrium Critical Behavior of the Two-Dimensional Ising Model

The influence of various initial magnetizations m0 and structural defects on the nonequilibrium critical behavior of the two-dimensional Ising model is numerically simulated by Monte Carlo methods. Based on analysis of the time dependence of magnetization and the two-time dependences of autocorrelation function and dynamic susceptibility, we revealed the influence of logarithmic corrections and the crossover phenomena of percolation behavior on the nonequilibrium characteristics and the critical exponents. Violation of the fluctuation–dissipation theorem is studied, and the limiting fluctuation–dissipation ratio is calculated for the case of high-temperature initial state. The influence of various initial states on the limiting fluctuation–dissipation ratio is investigated. The nonequilibrium critical dynamics of weakly disordered systems with spin concentrations p ≥ 0.9 is shown to belong to the universality class of the nonequilibrium critical behavior of the pure model and to be characterized by the same critical exponents and the same limiting fluctuation–dissipation ratios. The nonequilibrium critical behavior of systems with p ≤ 0.85 demonstrates that the universal characteristics of the nonequilibrium critical behavior depend on the defect concentration and the dynamic scaling is violated, which is related to the influence of the crossover effects of percolation behavior.

Non-equilibrium critical dynamics of bursts in θ and δ rhythms as fundamental characteristic of sleep and wake micro-architecture.

Origin and functions of intermittent transitions among sleep stages, including short awakenings and arousals, constitute a challenge to the current homeostatic framework for sleep regulation, focusing on factors modulating sleep over large time scales. Here we propose that the complex micro-architecture characterizing the sleep-wake cycle results from an underlying non-equilibrium critical dynamics, bridging collective behaviors across spatio-temporal scales. We investigate θ and δ wave dynamics in control rats and in rats with lesions of sleep-promoting neurons in the parafacial zone. We demonstrate that intermittent bursts in θ and δ rhythms exhibit a complex temporal organization, with long-range power-law correlations and a robust duality of power law (θ-bursts, active phase) and exponential-like (δ-bursts, quiescent phase) duration distributions, typical features of non-equilibrium systems self-organizing at criticality. Crucially, such temporal organization relates to anti-correlated coupling between θ- and δ-bursts, and is independent of the dominant physiologic state and lesions, a solid indication of a basic principle in sleep dynamics.

Critical Dynamics and Coupling in Bursts of Cortical Rhythms Indicate Non-Homeostatic Mechanism for Sleep-Stage Transitions and Dual Role of VLPO Neurons in Both Sleep and Wake.

Origin and functions of intermittent transitions among sleep stages, including brief awakenings and arousals, constitute a challenge to the current homeostatic framework for sleep regulation, focusing on factors modulating sleep over large time scales. Here we propose that the complex micro-architecture characterizing sleep on scales of seconds and minutes results from intrinsic non-equilibrium critical dynamics. We investigate θ- and δ-wave dynamics in control rats and in rats where the sleep-promoting ventrolateral preoptic nucleus (VLPO) is lesioned (male Sprague-Dawley rats). We demonstrate that bursts in θ and δ cortical rhythms exhibit complex temporal organization, with long-range correlations and robust duality of power-law (θ-bursts, active phase) and exponential-like (δ-bursts, quiescent phase) duration distributions, features typical of non-equilibrium systems self-organizing at criticality. We show that such non-equilibrium behavior relates to anti-correlated coupling between θ- and δ-bursts, persists across a range of time scales, and is independent of the dominant physiologic state; indications of a basic principle in sleep regulation. Further, we find that VLPO lesions lead to a modulation of cortical dynamics resulting in altered dynamical parameters of θ- and δ-bursts and significant reduction in θ-δ coupling. Our empirical findings and model simulations demonstrate that θ-δ coupling is essential for the emerging non-equilibrium critical dynamics observed across the sleep-wake cycle, and indicate that VLPO neurons may have dual role for both sleep and arousal/brief wake activation. The uncovered critical behavior in sleep- and wake-related cortical rhythms indicates a mechanism essential for the micro-architecture of spontaneous sleep-stage and arousal transitions within a novel, non-homeostatic paradigm of sleep regulation.SIGNIFICANCE STATEMENT We show that the complex micro-architecture of sleep-stage/arousal transitions arises from intrinsic non-equilibrium critical dynamics, connecting the temporal organization of dominant cortical rhythms with empirical observations across scales. We link such behavior to sleep-promoting neuronal population, and demonstrate that VLPO lesion (model of insomnia) alters dynamical features of θ and δ rhythms, and leads to significant reduction in θ-δ coupling. This indicates that VLPO neurons may have dual role for both sleep and arousal/brief wake control. The reported empirical findings and modeling simulations constitute first evidences of a neurophysiological fingerprint of self-organization and criticality in sleep- and wake-related cortical rhythms; a mechanism essential for spontaneous sleep-stage and arousal transitions that lays the bases for a novel, non-homeostatic paradigm of sleep regulation.

Nonequilibrium critical dynamics in the quantum chiral clock model

In this paper we study the driven critical dynamics in the three-state quantum chiral clock model. This is motivated by a recent experiment, which verified the Kibble-Zurek mechanism and the finite-time scaling in a reconfigurable one-dimensional array of $^{87}$Rb atoms with programmable interactions. This experimental model shares the same universality class with the quantum chiral clock model and has been shown to possess a nontrivial non-integer dynamic exponent $z$. Besides the case of changing the transverse field as realized in the experiment, we also consider the driven dynamics under changing the longitudinal field. For both cases, we verify the finite-time scaling for a non-integer dynamic exponent $z$. Furthermore, we determine the critical exponents $\beta$ and $\delta$ numerically for the first time. We also investigate the dynamic scaling behavior including the thermal effects, which are inevitably involved in experiments. From a nonequilibrium dynamic point of view, our results strongly support that there is a direct continuous phase transition between the ordered phase and the disordered phase. Also, we show that the method based on the finite-time scaling theory provides a promising approach to determine the critical point and critical properties.

Nonuniversal critical aging scaling in three-dimensional Heisenberg antiferromagnets

We numerically investigate the stationary and non-equilibrium critical dynamics in three-dimensional isotropic Heisenberg antiferromagnets. Since the non-conserved staggered magnetization couples dynamically to the conserved magnetization density, we employ a hybrid simulation algorithm that combines reversible spin precession with relaxational Kawasaki spin exchange processes. We measure the dynamic critical exponent and identify a suitable intermediate time window to obtain the aging scaling exponents. Our results support an earlier renormalization group prediction: While the critical aging collapse exponent assumes a universal value, the associated temporal decay exponent in the two-time spin autocorrelation function depends on the initial distribution of the conserved fields; here, specifically on the width of the initial spin orientation distribution.

Nonequilibrium critical dynamics of low-dimensional frustrated magnets and multilayer structures

A Monte Carlo simulation of the non-equilibrium behavior of multilayer magnetic nanostructure is carried out. Equilibrium properties, critical temperatures Tc and hysteresis effects were studied for various thicknesses of ferromagnetic layers. It is shown that, in contrast to bulk magnetic systems, the aging effects in nanostructure arise not only at the ferromagnetic ordering temperature Tc but also within a wide temperature range at T ≤ Tc. Simulation of transport properties in multilayer structure permitted to calculate non-equilibrium values of magnetoresistance.

Non-equilibrium critical dynamics of low-dimensional magnetics and multilayer structures

The Monte Carlo simulation of the critical behavior of multilayer structures based on anisotropic Heisenberg model is performed. The influence of the uniaxial anisotropy on the critical behavior of the thin Heisenberg-like film is described. The investigation of non-equilibrium critical behavior of multilayer structure which correspond to the nanoscale superlattice Co/Cu demonstrates that the aging effects can be observed in a wider temperature range than for bulk magnetic systems.

Nonequilibrium critical dynamics of the two-dimensional Ashkin-Teller model at the Baxter line.

We investigate the short-time universal behavior of the two-dimensional Ashkin-Teller model at the Baxter line by performing time-dependent Monte Carlo simulations. First, as preparatory results, we obtain the critical parameters by searching the optimal power-law decay of the magnetization. Thus, the dynamic critical exponents θ_{m} and θ_{p}, related to the magnetic and electric order parameters, as well as the persistence exponent θ_{g}, are estimated using heat-bath Monte Carlo simulations. In addition, we estimate the dynamic exponent z and the static critical exponents β and ν for both order parameters. We propose a refined method to estimate the static exponents that considers two different averages: one that combines an internal average using several seeds with another, which is taken over temporal variations in the power laws. Moreover, we also performed the bootstrapping method for a complementary analysis. Our results show that the ratio β/ν exhibits universal behavior along the critical line corroborating the conjecture for both magnetization and polarization.

Renormalization group description of the nonequilibrium critical dynamics of spin systems at the fixed space dimension d = 3

We present the method and results of a renormalization group description of nonequilibrium critical relaxation of model A with evolution from an initial high-temperature state. We calculate the two-time dependence of the correlation function and response function and find a violation of the fluctuationdissipation theorem in the nonequilibrium critical regime. For the limit fluctuation-dissipation relation, which is a universal property of the nonequilibrium critical dynamics, we calculate the fluctuation and impurity corrections in the two-loop approximation at the fixed space dimension d = 3 using Pade–Borel summation for asymptotic series.

Renormalization group description of the nonequilibrium critical dynamics of spin systems at the fixed space dimension $d=3$

Представлены методика и результаты ренормгруппового описания неравновесной критической релаксации модели А с эволюцией из начального высокотемпературного состояния. Рассчитана двухвременная зависимость для корреляционной функции и функции отклика и выявлены нарушения флуктуационно-диссипативной теоремы в неравновесном критическом режиме. Для предельного флуктуационно-диссипативного отношения, являющегося универсальной характеристикой неравновесной критической динамики, проведен в двухпетлевом приближении расчет флуктуационных и примесных поправок при фиксированной размерности пространства $d=3$ с применением методов суммирования асимптотических рядов Паде-Бореля.

Features of the Non-equilibrium Critical Dynamics in 3D Pure and Diluted Ising-like Ferromagnets

Features of the Non-equilibrium Critical Dynamics in 3D Pure and Diluted Ising-like Ferromagnets

Influence of disorder on ageing and memory effects in non-equilibrium critical dynamics of 3D Ising model relaxing from an ordered state

We have performed a numerical investigation of the influence of disorder on the dynamical non-equilibrium evolution of a 3D site-diluted Ising model from a low-temperature initial state with magnetization m0 = 1. It is shown that two-time dependences of the autocorrelation and integrated response functions for systems with spin concentrations p = 1.0, 0.95, 0.8, 0.6 and 0.5 demonstrate ageing properties with anomalous slowing-down relaxation and violation of the fluctuation-dissipation ratio. It was revealed that during non-equilibrium critical dynamics in the long-time regime the autocorrelation functions for diluted systems are extremely slow due to the pinning of domain walls on impurity sites. We have found that the fluctuation-dissipation ratio for diluted systems with spin concentration p < 1 while the pure system is characterized by . The autocorrelation function power-law delay becomes the same as for the time dependence of the magnetization in the critical point and is characterized by exponent . Also, for diluted systems we reveal memory effects for critical evolution in the ageing regime with realization of cyclic temperature change and quenching at .

Nonequilibrium critical dynamics of two dimensional interacting monomer-dimer model: non-Ising criticality

We investigate the nonequilibrium relaxation dynamics of an interacting monomer-dimer model with nearest neighbor repulsion on a square lattice, which possesses two symmetric absorbing states. The model is known to exhibit two nearby continuous transitions: the Z2 symmetry-breaking order-disorder transition and the absorbing transition with directed percolation criticality. We performed a more detailed analysis of our extensive simulations on bigger lattice systems which reaffirms that the symmetry-breaking transition exhibits a non-Ising critical behavior with β ≃ 0.149(2) and η ≃ 0.30(1) that are distinct from those values of a pure two dimensional Ising model. Finite size scaling of dimer density near the symmetry breaking transition gives logarithmic scaling (α = 0.0) which is consistent with the hyperscaling relation but the corresponding exponent of νB ≃ 1.37(2) exhibits a conspicuous deviation from the pure Ising value of 1. The value of dynamic critical exponent z, however, is found to be close to that of the kinetic Ising model as 1/z ≃ 0.466(5) from the relaxation of staggered magnetization (and also similar but slightly smaller values from coarsening).

Ageing and non-equilibrium critical phenomena in Monte Carlo simulations

It is considered the non-equilibrium critical evolution of statistical systems which displays some features, such as ageing and violation of the fluctuation-dissipation theorem. We review here some theoretical results of computations that have been obtained in recent years for universal quantities, such as the exponents determining the scaling behaviour of dynamic response and correlation functions and the fluctuation-dissipation ratio, associated with the non-equilibrium critical dynamics, with particular focus on the 3D pure and diluted Ising models with Glauber dynamics. We analyse an influence of critical fluctuations, different non-equilibrium initial states and presence of nonmagnetic impurities in spin systems on two-time dependence of correlation and response functions on characteristic time variables as waiting time tw and time of observation t – tw with t > tw. We discuss the obtained values of non-equilibrium exponents for autocorrelation and response functions and values of the universal long-time limit of the fluctuation-dissipation ratio X∞. Analysis of simulation results show that the insertion of disorder leads to new values of X∞ with X∞diluted > X∞pure.

Non-equilibrium critical dynamics of pure and diluted 2D XY-model

Comprehensive study of the ageing and the violation of the fluctuation-dissipation theorem in a pure and diluted two-dimensional XY-model were carried out. Two-dimensional XY-model tend to a particular type of phase transition is called a phase transition Berezinskii-Kosterlitz-Thouless associated with the change of the correlation properties of the system.

Asymmetry and basic pathways in sleep-stage transitions

We study dynamical aspects of sleep micro-architecture. We find that sleep dynamics exhibits a high degree of asymmetry, and that the entire class of sleep-stage transition pathways underlying the complexity of sleep dynamics throughout the night can be characterized by two independent asymmetric transition paths. These basic pathways remain stable under sleep disorders, even though the degree of asymmetry is significantly reduced. Our findings demonstrate an intriguing temporal organization in sleep micro-architecture at short time scales that is typical for physical systems exhibiting self-organized criticality (SOC), and indicates nonequilibrium critical dynamics in brain activity during sleep.