Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1010.4366 · Physica Scripta

Non-equilibrium phase transition in the kinetic Ising model driven by a propagating magnetic field wave

Muktish Acharyya

Published Sep 1, 2011• 10 citations
arXivHTMLPDF

Abstract

The two-dimensional ferromagnetic Ising model in the presence of a propagating magnetic field wave (with a well-defined frequency and wavelength) was studied by Monte Carlo simulation. This study differs from similar earlier studies, because in earlier studies the oscillating magnetic field was considered to be uniform in space. The time averaged magnetization over a full cycle (the time period) of the propagating magnetic field acted as the dynamic order parameter. The dynamical phase transition was observed. The temperature variation of the dynamic order parameter, the mean square deviation of the dynamic order parameter, the dynamic specific heat and the derivative of the dynamic order parameter were studied. The mean square deviation of the dynamic order parameter and the dynamic specific heat show sharp maxima near the transition point. The derivative of the dynamic order parameter shows a sharp minimum near the transition point. The transition temperature is found to depend also on the speed of propagation of the magnetic field wave.

DOI
10.1088/0031-8949/84/03/035009

Related papers

Nonequilibrium Phase Transition in Spin- S Ising Ferromagnet Driven by Propagating and Standing Magnetic Field Wave

Ajay Halder, Muktish Acharyya

Abstract The dynamical response of spin-S (S=1, 3/2, 2, 3) Ising ferromagnet to the plane propagating wave, standing magnetic field wave and uniformly oscillating field with constant frequency are studied separately in two dimensions by extensive Monte Carlo simulation. Depending upon the strength of the magnetic field and the value of the spin state of the Ising spin lattice two different dynamical phases are observed. For a fixed value of S and the amplitude of the propagating magnetic field wave the system undergoes a dynamical phase transition from propagating phase to pinned phase as the temperature of the system is cooled down. Similarly in case with standing magnetic wave the system undergoes dynamical phase transition from high temperature phase where spins oscillate coherently in alternate bands of half wavelength of the standing magnetic wave to the low temperature pinned or spin frozen phase. For a fixed value of the amplitude of magnetic field oscillation the transition temperature is observed to decrease to a limiting value as the value of spin S is increased. The time averaged magnetisation over a full cycle of the magnetic field oscillation plays the role of the dynamic order parameter. A comprehensive phase boundary is drawn in the plane of magnetic field amplitude and dynamic transition temperature. It is found that the phase boundary shrinks inwards for high value of spin state S. Also in the low temperature (and high field) region the phase boundaries are closely spaced.

arXiv:1707.04404•Communications in Theoretical Physics•Nov 1, 2017•4 citations

Polarised Electromagnetic Wave Propagation Through the Ferromagnet: Phase Boundary of Dynamic Phase Transition

Muktish Acharyya

The dynamical responses of ferromagnet to the propagating electromagnetic field wave passing through it are modelled and studied here by Monte Carlo simulation in two dimensional Ising ferromagnet. Here, the electromagnetic wave is linearly polarised in such a way that the direction of magnetic field is parallel to that of the magnetic momemts (spins). The coherent propagating mode of spin-clusters is observed. The time average magnetisation over the full cycle (time) of the field defines the order parameter of the dynamic transition. Depending on the value of the temperature and the amplitude of the propagating magnetic field wave, a dynamical phase transition is observed. The dynamic transition was detected by studying the temperature dependences of the dynamic order parameter, the variance of the dynamic order parameter, the derivative of the dynamic order parameter and the dynamic specific heat. The phase boundaries of the dynamic transitions were drawn for two different values of the wave lengths of the propagating magnetic field wave. The phase boundary was observed to shrink (inward) for lower speed of propagation of the EM wave. The divergence of the releavant length scale was observed at the transition point.

arXiv:1301.3071•Acta Physica Polonica B•Jan 1, 2014•9 citations

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

Muktish Acharyya

The nonequilibrium dynamic phase transition, in the kinetic Ising model in the 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 magnetization. In both cases, the Debye ``relaxation'' behavior 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 appropriately defined ``specific heat'' is studied by the Monte Carlo simulation near the transition point. The specific heat has been observed to diverge near the dynamic transition point.

arXiv:cond-mat/9611181•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Sep 1, 1997•96 citations

Nonequilibrium phase transition in the kinetic Ising model: Violation of Fluctuation-Dissipation relation

Muktish Acharyya

The nonequilibrium dynamic phase transition, in the kinetic Ising model in presence of an oscillating magnetic field, has been studied by Monte Carlo simulation. The fluctuation of dynamic order parameter has been studied as a function of temperature near the dynamic transition point. The temperature variation of appropriately defined `susceptibility' has also been studied near the dynamic transition point. Similarly, fluctuation of energy and appropriately defined `specific-heat' have been studied as a function of temperature near the dynamic transition point. In both the cases, the fluctuations (of dynamic order parameter and energy) and the corresponding responses diverge (as power law fashion) near the dynamic transition point with similar critical behavior (with identical exponent values).

arXiv:cond-mat/9701180•Jan 24, 1997•0 citations

Universality Class of the Nonequilibrium Phase Transition in Two-Dimensional Ising Ferromagnet Driven by Propagating Magnetic Field Wave

Ajay Halder, Muktish Acharyya

The purpose of this work is to identify the universality class of the nonequilibrium phase transition in the two-dimensional kinetic Ising ferromagnet driven by propagating magnetic field wave. To address this issue, the finite size analysis of the nonequilibrium phase transition, in two-dimensional Ising ferromagnet driven by plane propagating magnetic wave, is studied by Monte Carlo simulation. It is observed that the system undergoes a nonequilibrium dynamic phase transition from a high temperature dynamically symmetric (propagating) phase to a low temperature dynamically symmetry-broken (pinned) phase as the system is cooled below the transition temperature. This transition temperature is determined precisely by studying the fourth-order Binder Cumulant of the dynamic order parameter as a function of temperature for different system sizes (L). From the finite size analysis of dynamic order parameter and the dynamic susceptibility , we have estimated the critical exponents and (measured from the data read at the critical temperature obtained from Binder cumulant), and (measured from the peak positions of dynamic susceptibility). Our results indicate that such driven Ising ferromagnet belongs to the same universality class of the two-dimensional equilibrium Ising ferromagnet (where and ), within the limits of statistical errors.

arXiv:1805.02389•Applied Mathematics•Jan 1, 2019•0 citations

Dynamic phase transition properties of kinetic Ising model in the presence of additive white noise

Yusuf Yüksel

Using Monte Carlo simulations based on the Metropolis algorithm, we investigate the dynamic phase transition properties of kinetic Ising model driven by a sinusoidally oscillating magnetic field in the presence of additive white noise. We calculate equilibrium and dynamic properties such as the temperature dependence of average magnetization and magnetic specific heat, as well as the period dependence of dynamic order parameter and scaled variance. After determining the critical period at which order-disorder transition takes place, we perform finite size scaling analysis to extract the exponent ratios, and discuss the variation of these properties in the presence of noisy magnetic field. As a general result, we show that for a noisy system, DPT does not fall into a universality class of the conventional dynamic (and also equilibrium) universality class of the Ising model.

arXiv:1807.03077•Jul 9, 2018•0 citations
The two-dimensional ferromagnetic Ising model in the presence of a propagating magnetic field wave (with a well-defined frequency and wavelength) was studied by Monte Carlo simulation. This study differs from similar earlier studies, because in earlier studies the oscillating magnetic field was considered to be uniform in space. The time averaged magnetization over a full cycle (the time period) of the propagating magnetic field acted as the dynamic order parameter. The dynamical phase transition was observed. The temperature variation of the dynamic order parameter, the mean square deviation of the dynamic order parameter, the dynamic specific heat and the derivative of the dynamic order parameter were studied. The mean square deviation of the dynamic order parameter and the dynamic specific heat show sharp maxima near the transition point. The derivative of the dynamic order parameter shows a sharp minimum near the transition point. The transition temperature is found to depend also on the speed of propagation of the magnetic field wave.
Abstract The dynamical response of spin-S (S=1, 3/2, 2, 3) Ising ferromagnet to the plane propagating wave, standing magnetic field wave and uniformly oscillating field with constant frequency are studied separately in two dimensions by extensive Monte Carlo simulation. Depending upon the strength of the magnetic field and the value of the spin state of the Ising spin lattice two different dynamical phases are observed. For a fixed value of S and the amplitude of the propagating magnetic field wave the system undergoes a dynamical phase transition from propagating phase to pinned phase as the temperature of the system is cooled down. Similarly in case with standing magnetic wave the system undergoes dynamical phase transition from high temperature phase where spins oscillate coherently in alternate bands of half wavelength of the standing magnetic wave to the low temperature pinned or spin frozen phase. For a fixed value of the amplitude of magnetic field oscillation the transition temperature is observed to decrease to a limiting value as the value of spin S is increased. The time averaged magnetisation over a full cycle of the magnetic field oscillation plays the role of the dynamic order parameter. A comprehensive phase boundary is drawn in the plane of magnetic field amplitude and dynamic transition temperature. It is found that the phase boundary shrinks inwards for high value of spin state S. Also in the low temperature (and high field) region the phase boundaries are closely spaced.
The dynamical responses of ferromagnet to the propagating electromagnetic field wave passing through it are modelled and studied here by Monte Carlo simulation in two dimensional Ising ferromagnet. Here, the electromagnetic wave is linearly polarised in such a way that the direction of magnetic field is parallel to that of the magnetic momemts (spins). The coherent propagating mode of spin-clusters is observed. The time average magnetisation over the full cycle (time) of the field defines the order parameter of the dynamic transition. Depending on the value of the temperature and the amplitude of the propagating magnetic field wave, a dynamical phase transition is observed. The dynamic transition was detected by studying the temperature dependences of the dynamic order parameter, the variance of the dynamic order parameter, the derivative of the dynamic order parameter and the dynamic specific heat. The phase boundaries of the dynamic transitions were drawn for two different values of the wave lengths of the propagating magnetic field wave. The phase boundary was observed to shrink (inward) for lower speed of propagation of the EM wave. The divergence of the releavant length scale was observed at the transition point.
The nonequilibrium dynamic phase transition, in the kinetic Ising model in the 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 magnetization. In both cases, the Debye ``relaxation'' behavior 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 appropriately defined ``specific heat'' is studied by the Monte Carlo simulation near the transition point. The specific heat has been observed to diverge near the dynamic transition point.
The nonequilibrium dynamic phase transition, in the kinetic Ising model in presence of an oscillating magnetic field, has been studied by Monte Carlo simulation. The fluctuation of dynamic order parameter has been studied as a function of temperature near the dynamic transition point. The temperature variation of appropriately defined `susceptibility' has also been studied near the dynamic transition point. Similarly, fluctuation of energy and appropriately defined `specific-heat' have been studied as a function of temperature near the dynamic transition point. In both the cases, the fluctuations (of dynamic order parameter and energy) and the corresponding responses diverge (as power law fashion) near the dynamic transition point with similar critical behavior (with identical exponent values).
The purpose of this work is to identify the universality class of the nonequilibrium phase transition in the two-dimensional kinetic Ising ferromagnet driven by propagating magnetic field wave. To address this issue, the finite size analysis of the nonequilibrium phase transition, in two-dimensional Ising ferromagnet driven by plane propagating magnetic wave, is studied by Monte Carlo simulation. It is observed that the system undergoes a nonequilibrium dynamic phase transition from a high temperature dynamically symmetric (propagating) phase to a low temperature dynamically symmetry-broken (pinned) phase as the system is cooled below the transition temperature. This transition temperature is determined precisely by studying the fourth-order Binder Cumulant of the dynamic order parameter as a function of temperature for different system sizes (L). From the finite size analysis of dynamic order parameter and the dynamic susceptibility , we have estimated the critical exponents and (measured from the data read at the critical temperature obtained from Binder cumulant), and (measured from the peak positions of dynamic susceptibility). Our results indicate that such driven Ising ferromagnet belongs to the same universality class of the two-dimensional equilibrium Ising ferromagnet (where and ), within the limits of statistical errors.
Using Monte Carlo simulations based on the Metropolis algorithm, we investigate the dynamic phase transition properties of kinetic Ising model driven by a sinusoidally oscillating magnetic field in the presence of additive white noise. We calculate equilibrium and dynamic properties such as the temperature dependence of average magnetization and magnetic specific heat, as well as the period dependence of dynamic order parameter and scaled variance. After determining the critical period at which order-disorder transition takes place, we perform finite size scaling analysis to extract the exponent ratios, and discuss the variation of these properties in the presence of noisy magnetic field. As a general result, we show that for a noisy system, DPT does not fall into a universality class of the conventional dynamic (and also equilibrium) universality class of the Ising model.