Kinetic Ising Model in an Oscillating Field: Finite-Size Scaling at the Dynamic Phase Transition

Sides, Scott; Rikvold, Per Arne; Novotny, M. A.

doi:10.1103/physrevlett.81.834

Cited by 214 publications

(201 citation statements)

References 26 publications

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“…Based on this result, we expect that the catalytic activity of the system will increase when the system is subjected to periodic variation of the external CO pressure, only when one takes into account that the time it takes the system to decontaminate is different from the time it takes it to contaminate. Furthermore, we show that the ZGB-k model, driven by an oscillating CO pressure, undergoes a dynamic phase transition, similar to the one observed in Ising [18,19,22,23,24,25,26], anisotropic Heisenberg [27,28], and XY models [29], driven by an oscillating applied field.…”

Section: Introductionmentioning

confidence: 85%

“…This behavior suggests that for low values of k, the system has a dynamic phase transition (DPT) between a high CO 2 productive dynamic phase and a nonproductive one. This is reminiscent of the behavior of ferromagnetic Ising or anisotropic XY or Heisenberg spin systems driven by a periodically oscillating field [18,19,20,21,22,23,24,25,26,27,28,29].…”

Section: Resultsmentioning

confidence: 99%

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

et al. 2005

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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 CO 2 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 CO 2 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 β/ν ≈ 0.12 and γ/ν ≈ 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.

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Section: Introductionmentioning

confidence: 85%

Section: Resultsmentioning

confidence: 99%

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

et al. 2005

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“…They indicate that great caution must be shown in formulating and interpreting stochastic models of physical systems, as even seemingly minor modifications of the transition probabilities can significantly affect the nucleation rates. It might thus be interesting to investigate the influence of the specific stochastic dynamic on dynamic phase transitions in kinetic Ising models [26]. We also note that, although our results are derived for a specific model system, qualitatively similar results should apply to kinetic MC simulations for nucleation in a wide range of scientific disciplines.…”

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confidence: 88%

Low-Temperature Nucleation in a Kinetic Ising Model with Soft Stochastic Dynamics

et al. 2004

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We study low-temperature nucleation in kinetic Ising models by analytical and simulational methods, confirming the general result for the average metastable lifetime, τ = A exp(βΓ) (β = 1/kBT ) [E. Jordão Neves and R. H. Schonmann, Commun. Math. Phys. 137, 209 (1991)]. Contrary to common belief, we find that both A and Γ depend significantly on the stochastic dynamic. In particular, for a "soft" dynamic, in which the effects of the interactions and the applied field factorize in the transition rates, Γ does not simply equal the energy barrier against nucleation, as it does for the standard Glauber dynamic, which does not have this factorization property. [7], and atmospheric science [8], to mention just a few. However, many questions in nucleation theory are still unresolved, and recently there has been much interest in kinetic Ising systems as models for nucleation. In particular, much work has been done on their dynamical behavior at very low temperatures [9,10,11,12,13,14], where it is influenced by lattice discreteness. It is then possible to calculate exactly both the shape of the critical nucleus (the saddle-point configuration) and the most probable path during a nucleation event. In a typical numerical experiment, the system is prepared in a metastable state with all spins positive in a negative applied field. During each MC step (MCS), a randomly chosen spin is flipped with a configuration-dependent transition rate W that satisfies detailed balance, so that it will drive the system to thermodynamic equilibrium. The metastable lifetime is measured as the average number of MCS until the magnetization reaches zero. In the regime of singledroplet decay studied here, the lifetime measured in MCS is independent of the system size [9,11,15]. In the lowtemperature limit the lifetime has been rigorously shown to be [9] τ = Ae βΓ .(Here the only dependence on the temperature T is through β = 1/k B T , where k B is Boltzmann's constant (hereafter set equal to one). It is often assumed that Γ equals the energy difference between the saddle point and the metastable state [13,14], independent of the specific stochastic dynamic. In this Letter we show that this is not always so. In particular, we describe two dynamics that both obey detailed balance but have different values of Γ and A for all values of the applied field, despite having the same saddle-point configuration.At sufficiently low T , the saddle point was shown in Ref.[9] to be an ℓ × (ℓ − 1) rectangle of overturned spins with a "knob" of one overturned spin on one of its long sides. The critical length ℓ = ⌊2J/|H|⌋ + 1 for all |H| ∈ (0, 4), where ⌊x⌋ is the integer part of x. Here, J > 0 is the nearest-neighbor interaction constant of the Ising model, which will henceforth be set to unity. The critical length thus changes discontinuously at values of |H| such that 2/|H| is an integer.The square-lattice S = 1/2 Ising ferromagnet with unit interaction is defined by the Hamiltonian H = − α,β σ α σ β − H α σ α , where the Ising spins σ α = ±1, H is the applie...

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“…The nonequilibrium dynamic phase transition and the hysteretic response are the main characteristic features of the ferromagnetic system driven by time dependent magnetic field. Some observations or studies regarding -(i) divergences of dynamic specific heat and relaxation time near transition point [3,4], (ii) divergence of the relevant length scale near transition point [5], (iii) studies regarding existence of tricritical point [6,7], (iv) its relation with stochastic resonance [6], and the hysteresis loss [8] etc., establish that the dynamic phase transition is similar in many aspects to the well known equilibrium thermodynamic phase transition. This fact is further supported by some experimental findings like-(i) detection of dynamic phase transition in the ultra-thin Co film on Cu(001) system by surface magneto-optic Kerr effect [9,10], (ii) direct excitation of propagating spin waves by focussed ultra short optical pulse [11], (iii) the transient behaviour of dynamically ordered phase in uniaxial cobalt film [12] etc.…”

Section: Introductionmentioning

confidence: 99%

Standing magnetic wave on Ising ferromagnet: Nonequilibrium phase transition

Halder¹,

Acharyya²

2016

Journal of Magnetism and Magnetic Materials

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The dynamical response of an Ising ferromagnet to a plane polarised standing magnetic field wave is modelled and studied here by Monte Carlo simulation in two dimensions. The amplitude of standing magnetic wave is modulated along the direction x. We have detected two main dynamical phases namely, pinned and oscillating spin clusters. Depending on the value of field amplitude the system is found to undergo a phase transition from oscillating spin cluster to pinned as the system is cooled down. The time averaged magnetisation over a full cycle of magnetic field oscillations is defined as the dynamic order parameter. The transition is detected by studying the temperature dependences of the variance of the dynamic order parameter, the derivative of the dynamic order parameter and the dynamic specific heat. The dependence of the transition temperature on the magnetic field amplitude and on the wavelength of the magnetic field wave is studied at a single frequency. A comprehensive phase boundary is drawn in the plane described by the temperature and field amplitude for two different wavelengths of the magnetic wave. The variation of instantaneous line magnetisation during a period of magnetic field oscillation for standing wave mode is compared to those for the propagating wave mode. Also the probability that a spin at any site, flips, is calculated. The above mentioned variations and the probability of spin flip clearly distinguish between the dynamical phases formed by propagating magnetic wave and by standing magnetic wave in an Ising ferromagnet.

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Kinetic Ising Model in an Oscillating Field: Finite-Size Scaling at the Dynamic Phase Transition

Cited by 214 publications

References 26 publications

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

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

Low-Temperature Nucleation in a Kinetic Ising Model with Soft Stochastic Dynamics

Standing magnetic wave on Ising ferromagnet: Nonequilibrium phase transition

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