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

Acharyya, Muktish

doi:10.1103/physreve.56.2407

Cited by 96 publications

(83 citation statements)

References 10 publications

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“…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%

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: 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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“…It was then studied further, both in mean-field models [3,4,5,6] and in kinetic Monte Carlo (KMC) simulations [5,6,7,8,9,10]. A review of this early work can be found in Ref.…”

Section: Introductionmentioning

confidence: 99%

Conjugate field and fluctuation-dissipation relation for the dynamic phase transition in the two-dimensional kinetic Ising model

et al. 2007

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The two-dimensional kinetic Ising model, when exposed to an oscillating applied magnetic field, has been shown to exhibit a nonequilibrium, second-order dynamic phase transition (DPT), whose order parameter Q is the period-averaged magnetization. It has been established that this DPT falls in the same universality class as the equilibrium phase transition in the two-dimensional Ising model in zero applied field. Here we study for the first time the scaling of the dynamic order parameter with respect to a nonzero, period-averaged, magnetic 'bias' field, H b , for a DPT produced by a square-wave applied field. We find evidence that the scaling exponent,

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

Cited by 96 publications

References 10 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

Conjugate field and fluctuation-dissipation relation for the dynamic phase transition in the two-dimensional kinetic Ising model

Standing magnetic wave on Ising ferromagnet: Nonequilibrium phase transition

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