Nonequilibrium Dynamic Phase Transition Research Articles

Visualization of dynamic metastable states evolution in TiO2 memristor during electroforming by electroluminescence

The electroforming process, transforming a homogeneous insulating oxide into localized conductive filaments, is crucial for memristive devices. However, it is still unclear how the intermediate phases develop microscopically throughout the transient forming process. Here, we investigate the nonequilibrium dynamic phase transition in the conductive region of TiO2 memristors during electroforming. Synchronous electroluminescence emission and transport measurements demonstrate that the application of pulse fields primarily causes a gradual reduction in the conducting area, accompanied by the reversible field-dependent evolution of metastable phases at the cathode region. As a result of positive feedback between the lateral gradient of oxygen vacancies and the electric field, the self-reinforcing process eventually facilitates the final filament generation. This study offers insights into the physical mechanisms governing the metastable phase evolution during electroforming and raises implications for optimizing the forming process of memristive devices.

Effect of Li element on shocking behavior of Fe-Li alloys

Understanding the effect of alloying elements on shock behaviors is significant for constitutive model of alloy materials at under dynamic high pressure. However, an in-depth understanding about the microscopic mechanism of alloying elements effect on plasticity and phase transition is still limited. In this work, applying non-equilibrium molecular dynamic (NEMD) simulations, shock-induced plasticity and phase transition of Fe-Li alloys was investigated in terms of the compositions of Li, crystallographic direction and shock velocity. The results show that yield stress (or phase change pressure) of Fe-Li alloy was reduced doping Li element, and the large internal stresses caused by concentration of Li element effectively activated the nucleation and multiplication of dislocation loops. But with the increase of Li composition, phase transition is inhibited for shock along [111] direction because of stress release caused by multiplication of dislocation. There is a strong dependence between these microscopic processes and the law of plastic wave propagation. Moreover, with the increase of Li composition, the diversity of phase transition variants was inhibited for shock along [110] direction due to the destruction of initial stress and potential energy uniformity.

Dynamical phase transition characteristics of FeC2 monolayer

The nonequilibrium dynamic phase transition properties of a two dimensional FeC2 monolayer in the presence of a time dependent sinusoidally oscillating magnetic field have been studied by using both mean field approximation with Glauber type of stochastic process and Monte Carlo simulation technique. The variation of the Curie temperature of the system with the amplitude and period of the external magnetic field have been investigated and temperature dependence of the magnetization of the system is presented for selected external field parameters. Moreover, the dynamic hysteresis curves of the system have been obtained for a wide range of temperature. Numerical results of the present study indicate the controllability of the dynamic magnetic properties of two dimensional FeC2 sheet by amplitude and period of the external magnetic field.

Macroscopic yielding in jammed solids is accompanied by a nonequilibrium first-order transition in particle trajectories.

We use computer simulations to analyze the yielding transition during large-amplitude oscillatory shear of a simple model for soft jammed solids. Simultaneous analysis of global mechanical response and particle-scale motion demonstrates that macroscopic yielding, revealed by a smooth crossover in mechanical properties, is accompanied by a sudden change in the particle dynamics, which evolves from nondiffusive motion to irreversible diffusion as the amplitude of the shear is increased. We provide numerical evidence that this sharp change corresponds to a nonequilibrium first-order dynamic phase transition, thus establishing the existence of a well-defined microscopic dynamic signature of the yielding transition in amorphous materials in oscillatory shear.

Non-equilibrium phase transition properties of disordered binary ferromagnetic alloy

Non-equilibrium dynamic phase transition features of a disordered binary ferromagnetic alloy consisting of spin-1/2 and spin-1 components under the presence of a time dependent oscillating magnetic field have been analyzed for a two dimensional square lattice. With the help of Glauber-type stochastic process, the kinetic equations of time dependent magnetizations have been derived based on the effective-field theory with single-site correlations. A systematic analysis for the whole range of the concentrations of randomly distributed components as well as other system parameters has been carried out. According to our numerical investigations, the considered system presents unusual thermal and magnetic field behaviors such as the existence of dynamic multi-critical behavior and also boundaries of the coexistence region, where both dynamically ordered and disordered phases overlap, sensitively depends on the studied parameter space.

Nonequilibrium phase transitions and stationary-state solutions of a three-dimensional random-field Ising model under a time-dependent periodic external field

Nonequilibrium behavior and dynamic phase-transition properties of a kinetic Ising model under the influence of periodically oscillating random fields have been analyzed within the framework of effective-field theory based on a decoupling approximation. A dynamic equation of motion has been solved for a simple-cubic lattice (q=6) by utilizing a Glauber-type stochastic process. Amplitude of the sinusoidally oscillating magnetic field is randomly distributed on the lattice sites according to bimodal and trimodal distribution functions. For a bimodal type of amplitude distribution, it is found in the high-frequency regime that the dynamic phase diagrams of the system in the temperature versus field amplitude plane resemble the corresponding phase diagrams of the pure kinetic Ising model. Our numerical results indicate that for a bimodal distribution, both in the low- and high-frequency regimes, the dynamic phase diagrams always exhibit a coexistence region in which the stationary state (ferro or para) of the system is completely dependent on the initial conditions, whereas for a trimodal distribution, the coexistence region disappears depending on the values of the system parameters.

Noneqilibrium Phase Transition in Kinetic Ising Model: Absence of Tricritical behaviour in Presence of Impurities

The nonequilibrium dynamic phase transition, in the two dimensional site diluted kinetic Ising model in presence of an oscillating magnetic field, has been studied by Monte Carlo simulation. The projections of dynamical phase surface are drawn in the planes formed by the dilution and field amplitude and the plane formed by temperature and field amplitude. The tricritical behaviour is found to be absent in this case which was observed in the pure system.

Nonequilibrium dynamic phase transition in the ferromagnetic potts model

The nonequilibrium dynamic phase transition arises in various magnetic systems such as ferromagnetic Ising model when system is driven by both an external field and temperature simultaneously. In this paper, the nonequilibrium dynamic phase transition in the q-state Potts model in the presence of a time dependent oscillating magnetic field on a simple cubic lattice is investigated by mean field theory and time dependent Ginzburug-Landau equation. For the case of q = 2, with decrease of the temperature the system undergoes a dynamically ordered phase transition, which is characterized by the period averaged magnetization Q, from a dynamically disordered state Q = 0 to the dynamically ordered state Q ≠ 0. On the other hand, for the case of q = 3 the system has indicated more complicated behavior than that of q = 2. We investigated those characteristic features of the dynamical phase state from the behavior of the dynamic magnetization and the Liapunov exponent.

Dilute wet granular particles: Nonequilibrium dynamics and structure formation

We investigate a gas of wet granular particles covered by a thin liquid film. The dynamic evolution is governed by two-particle interactions, which are mainly due to interfacial forces in contrast to dry granular gases. When two wet grains collide, a capillary bridge is formed and stays intact up to a certain distance of withdrawal when the bridge ruptures, dissipating a fixed amount of energy. A freely cooling system is shown to undergo a nonequilibrium dynamic phase transition from a state with mainly single particles and fast cooling to a state with growing aggregates such that bridge rupture becomes a rare event and cooling is slow. In the early stage of cluster growth, aggregation is a self-similar process with a fractal dimension of the aggregates approximately equal to Df approximately 2 . At later times, a percolating cluster is observed which ultimately absorbs all the particles. The final cluster is compact on large length scales, but fractal with Df approximately 2 on small length scales.

Nonequilibrium dynamic phase transition in a kinetic Ising spin system

We studied within the framework of a mean-field approach the nonequilibrium dyn amic phase transition of a kinetic Ising spin system subject to a perturbative f ield and temperature simultaneously by comparison between time-dependent Ginzbur g-Landau and Glauber dynamics models. The dynamic phase transition (DPT) boundar ies, separating a symmetry-breaking dynamic ordered phase from its symmetric dyn amic disordered counterpart, were identified through a systematic simulation of the above two models. The dependence of the dynamic order parameter Q and the fo urth order cumulant ratio U upon the temperature t(r0), the frequency ω and amplitude h0 of driving field were also investigated in detai l. A discussion was presented concerning the current controversies on whether bo th a discontinuous dynamic phase transition occurs possibly below a specific low temperature and a tri-critical point exists on the DPT boundary in a kinetic Is ing spin system.

NONEQUILIBRIUM PHASE TRANSITIONS IN MODEL FERROMAGNETS: A REVIEW

The thermodynamical behaviors of ferromagnetic systems in equilibrium are well studied. However, the ferromagnetic systems far from equilibrium became an interesting field of research in last few decades. Recent exploration of ferromagnetic systems in the presence of a steady magnetic field are also studied by using standard tools of equilibrium statistical physics. The ferromagnet in the presence of time-dependent magnetic field, shows various interesting phenomena. An usual response of a ferromagnet in the presence of a sinusoidally oscillating magnetic field is the hysteresis. Apart from this hysteretic response, the nonequilibrium dynamic phase transition is also a very interesting phenomenon. In this chapter, the nonequilibrium dynamic phase transitions of the model ferromagnetic systems in presence of time-dependent magnetic field are discussed. For this kind of nonequilibrium phase transition, one cannot employ the standard techniques of equilibrium statistical mechanics. The recent developments in this direction are mainly based on numerical simulation (Monte Carlo). The Monte Carlo simulation of kinetic Ising model, in presence of sinusoidally oscillating (in time but uniform over space) magnetic field, is extensively performed to study the nonequilibrium dynamic phase transition. The temperature variations of dynamic order parameter, dynamic specific heat, dynamic relaxation time etc. near the transition point are discussed. The appearance and behaviors of a dynamic length scale and a dynamic time scale near the transition point are also discussed. All these studies indicate that this proposed dynamic transition is a nonequilibrium thermodynamic phase transition. The disorder (quenched) induced zero temperature (athermal) dynamic transition is studied in random field Ising ferromagnet. The dynamic transition in the Heisenberg ferromagnet is also studied. The nature of this transition in the Heisenberg ferromagnet depends on the anisotropy and the polarisation of the applied time varying magnetic field. The anisotropic Heisenberg ferromagnet in the presence of elliptically polarised magnetic field shows multiple dynamic transitions. This multiple dynamic transitions in anisotropic Heisenberg ferromagnet are discussed here. Recent experimental evidences of dynamic transitions are also discussed very briefly.

Stochastic resonance and nonequilibrium dynamic phase transition of Ising spin system driven by a joint external field

We studied the dynamic response and stochastic resonance of kinetic Ising spin system (ISS), subject to the joint external field of weak sinusoidal modulation and stochastic white-noise, through solving the mean-field equation of motion based on Glauber dynamics. The periodically driven stochastic ISS shows the occurrence of characteristic stochastic resonance as well as nonequilibrium dynamic phase transition (NDPT) when the frequency and amplitude h0 of driving field, the temperature t of the system and noise intensity D attain a specific accordance in quantity. There exist in the system two typical dynamic phases, referred to as dynamic disordered paramagnetic and ordered ferromagnetic phases respectively, corresponding to zero and unit dynamic order parameter. We also figured out the NDPT boundary surface of the system which separates the dynamic paramagnetic and dynamic ferromagnetic phase in the 3D parameter space of h0~t~D. An intriguing dynamical ferromagnetic phase with an intermediate order parameter at 0.66 was revealed for the first time in the ISS subject to the perturbation of a joint determinant and stochastic field. Our primary result indicates that the intermediate order dynamical ferromagnetic phase is dynamic metastable in nature and owns a peculiar characteristic in its stability and response to external driving field when compared with fully order dynamic ferromagnetic phase.

Response of a catalytic reaction to periodic variation of the CO pressure: IncreasedCO2production and dynamic phase transition

We present a kinetic Monte Carlo study of the dynamical response of a Ziff-Gulari-Barshad model for CO oxidation with CO desorption to periodic variation of the CO pressure. We use a square-wave periodic pressure variation with parameters that can be tuned to enhance the catalytic activity. We produce evidence that, below a critical value of the desorption rate, the driven system undergoes a dynamic phase transition between a CO2 productive phase and a nonproductive one at a critical value of the period and waveform of the pressure oscillation. At the dynamic phase transition the period-averaged CO2 production rate is significantly increased and can be used as a dynamic order parameter. We perform a finite-size scaling analysis that indicates the existence of power-law singularities for the order parameter and its fluctuations, yielding estimated critical exponent ratios beta/nu approximately 0.12 and gamma/nu approximately 1.77. These exponent ratios, together with theoretical symmetry arguments and numerical data for the fourth-order cumulant associated with the transition, give reasonable support for the hypothesis that the observed nonequilibrium dynamic phase transition is in the same universality class as the two-dimensional equilibrium Ising model.

Nonequilibrium dynamical phase transition of 3D kinetic Ising/Heisenberg spin system

We have studied the nonequilibrium dynamic phase transitions of both three-dimensional (3D) kinetic Ising and Heisenberg spin systems in the presence of a perturbative magnetic field by Monte Carlo simulation. The feature of the phase transition is characterized by studying the distribution of the dynamical order parameter. In the case of anisotropic Ising spin system (ISS), the dynamic transition is discontinuous and continuous under low and high temperatures respectively, which indicates the existence of a tri-critical point (TCP) on the phase \linebreak boundary separating low-temperature order phase and high-temperature disorder phase. The TCP shifts towards the higher temperature region with the decrease of frequency, i.e. TTCP=1.33×exp(−ω/30.7). In the case of the isotropic Heisenberg spin system (HSS), however, the situation on dynamic phase transition of HSS is quite different from that of ISS in that no stable dynamical phase transition was observed in kinetic HSS after a threshold time. The evolution of magnetization in the HSS driven by a symmetrical external field after a certain duration always tends asymptotically to a disorder state no matter what an initial state the system starts with. The threshold time τ depends upon the amplitude H0, reduced temperature T/TC and the frequency ω as τ = C.ωα.H0−β.(T/TC)−γ.

Nonequilibrium dynamic phase transition of an Ising spin system driven by various oscillating field

We have studied both the dynamic response and the relevant nonequilibrium dynami cal p hase transition of an Ising spin system subject to three sorts of oscillating fi eld i.e. sinusoidal, square and sawtooth waves. The above three sorts of externa l field drive dynamically the Ising spin system in either simply gradual ( abrupt) way or their combination respectively. In the case of both sinusoidal and squar e ways, it was observed that the Ising spin system displays a low_temperature sy mmetr y-breaking ordered phase and a high_temperature symmetric disordered phase as well as the dynamic transition between two dynamical phases above. We also detected the tri_critical point separating high_temperature continuous dynamic transition and low_temperature discontinuous one on the boundary of dynamic transition. The trend of dynamic transition boundary and the dependence of tri_critical point upon the system temperature, the frequency and amplitude of the driving field we re revea led as well. In contrast, nodynamic transition occurs any longer and the system always stays in symmetry-breaking ordered state if the external field takes the form of sawtooth wave. The preceding discrepancy in dynamic response and transi tion is attributed to the perturbative characteristic of different oscillating f ields.

Absence of first-order transition and tricritical point in the dynamic phase diagram of a spatially extended bistable system in an oscillating field.

It has been well established that spatially extended, bistable systems that are driven by an oscillating field exhibit a nonequilibrium dynamic phase transition (DPT). The DPT occurs when the field frequency is of the order of the inverse of an intrinsic lifetime associated with the transitions between the two stable states in a static field of the same magnitude as the amplitude of the oscillating field. The DPT is continuous and belongs to the same universality class as the equilibrium phase transition of the Ising model in zero field [G. Korniss et al., Phys. Rev. E 63, 016120 (2001); H. Fujisaka et al., Phys. Rev. E 63, 036109 (2001)]. However, it has previously been claimed that the DPT becomes discontinuous at temperatures below a tricritical point [M. Acharyya, Phys. Rev. E 59, 218 (1999)]. This claim was based on observations in dynamic Monte Carlo simulations of a multipeaked probability density for the dynamic order parameter and negative values of the fourth-order cumulant ratio. Both phenomena can be characteristic of discontinuous phase transitions. Here we use classical nucleation theory for the decay of metastable phases, together with data from large-scale dynamic Monte Carlo simulations of a two-dimensional kinetic Ising ferromagnet, to show that these observations in this case are merely finite-size effects. For sufficiently small systems and low temperatures, the continuous DPT is replaced, not by a discontinuous phase transition, but by a crossover to stochastic resonance. In the infinite-system limit, the stochastic-resonance regime vanishes, and the continuous DPT should persist for all nonzero temperatures.

Hysteresis and the dynamic phase transition in thin ferromagnetic films.

Hysteresis and the nonequilibrium dynamic phase transition in thin magnetic films subject to an oscillatory external field have been studied by Monte Carlo simulation. The model under investigation is a classical Heisenberg spin system with a bilinear exchange anisotropy Lambda in a planar thin film geometry with competing surface fields. The film exhibits a nonequilibrium phase transition between dynamically ordered and dynamically disordered phases characterized by a critical temperature T(cd), whose location is determined by the amplitude H0 and frequency omega of the applied oscillatory field. In the presence of competing surface fields the critical temperature of the ferromagnetic-paramagnetic transition for the film is suppressed from the bulk system value T(c) to the interface localization-delocalization temperature T(ci). The simulations show that in general T(cd)<T(ci) for the model film. The profile of the time-dependent layer magnetization across the film shows that the dynamically ordered and dynamically disordered phases coexist within the film for T<T(cd). In the presence of competing surface fields, the dynamically ordered phase is localized at one surface of the film.

Nonequilibrium phase transition in the kinetic Ising model: Is the transition point the maximum lossy point?

The nonequilibrium dynamic phase transition, in the kinetic Ising model in presence of an oscillating magnetic field, has been studied both by Monte Carlo simulation (in two dimensions) and by solving the mean-field dynamical equation of motion for the average magnetization. The temperature variations of hysteretic loss (loop area) and the dynamic correlation have been studied near the transition point. The transition point has been identified as the minimum-correlation point. The hysteretic loss becomes maximum above the transition point. An analytical formulation has been developed to analyze the simulation results. A general relationship among hysteresis loop area, dynamic order parameter, and dynamic correlation has also been developed.

Nonequilibrium phase transition in the kinetic Ising model: Dynamical symmetry breaking by randomly varying magnetic field

The nonequilibrium dynamic phase transition, in the two-dimensional kinetic Ising model in the presence of a randomly varying (in time but uniform in space) magnetic field, has been studied both by Monte Carlo simulation and by solving the mean-field dynamic equation of motion for the average magnetization. In both the cases, the time-averaged magnetization vanishes from a nonzero value depending upon the values of the width of randomly varying field and the temperature. The phase boundary lines are drawn in the plane formed by the width of the random field and the temperature.

Nonequilibrium phase transition in the kinetic Ising model: Critical slowing down and the specific-heat singularity

The nonequilibrium dynamic phase transition, in the kinetic Ising model in presence of an oscillating magnetic field, has been studied both by Monte Carlo simulation and by solving numerically the mean field dynamic equation of motion for the average magnetisation. In both the cases, the Debye 'relaxation' behaviour of the dynamic order parameter has been observed and the 'relaxation time' is found to diverge near the dynamic transition point. The Debye relaxation of the dynamic order parameter and the power law divergence of the relaxation time have been obtained from a very approximate solution of the mean field dynamic equation. The temperature variation of appropiately defined 'specific-heat' is studied by Monte Carlo simulation near the transition point. The specific-heat has been observed to diverge near the dynamic transition point.