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

Chinese Physics

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

Shao Yuan-Zhi, J.K.L. Lai, C.H. Shek, Lin Guang-ming, Lan Tu

Published Feb 1, 2004• 5 citations
Publisher

Abstract

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. T TCP =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 H 0 , reduced temperature T / T C and the frequency ω as τ = C .ω α . H 0 −β .( T / T C ) −γ .

DOI
10.1088/1009-1963/13/2/021

Related papers

Nonequilibrium Dynamical Phase Transition of a Three-Dimensional Kinetic Heisenberg Spin System

Shao Yuan-Zhi, J.K.L. Lai, C.H. Shek +2 more

We systematically investigate the dynamical response of a three-dimensional kinetic isotropic Heisenberg spin system (HSS) to an external driving field by Monte Carlo numerical simulation. The dynamical response of the isotropic HSS differs obviously from those of the anisotropic Ising spin system in which no real stable ordered state and relevant dynamical phase transition were observed in the kinetic HSS. There is a threshold time after which the magnetization m ( t ) in the HSS driven by a symmetrical external field always tends asymptotically to a disorder state regardless of the initial state of the system. The threshold time depends on the reduced temperature T / T C of the investigated spin system, amplitude H 0 and frequency of the external field, i.e. τ = C ·ω α · H 0 -β ·( T / T C ) -γ . C is a constant equal to 0.0302 for a three-dimensional lattice and exponents α = 1.18±0.01, β = 1.81±0.01 and γ = 1.68±0.01.

Chinese Physics Letters•Aug 22, 2002•1 citation

DYNAMICAL TRANSITION AND TRICRITICAL POINTS OF 3D KINETIC ISING SPIN SYSTEM

Shao Yuan-Zhi, Lan Tu, Lin Guang-ming +1 more

The dynamic phase transition has been studied in the three-dimensional kinetic Ising model in the presence of a time-varying(sinusoidal)magnetic field by Monte Carlo simulation.The nature of the transition is characterized by studying the distribution of the order parameter.The system is in contact with an isothermal heat bath at temperature T.We varied the magnitude of the magnetic field,keeping the frequency of the magnetic field unchanged.For the lower values of the environment temperature the transition is discontinuous and it is continuous for higher values of the environment temperature,indicating the existence of a tricritical point (TCP) on the phase boundary.The TCP shifts towards higher temperature region with the decrease of frequency.i.e:TTCP=1.33×e(-ω/30.7)

Acta Physica Sinica•Jan 1, 2001•1 citation

Nonequilibrium dynamic phase transition in a kinetic Ising spin system

Shao Yuan-Zhi, Zhong Wei-Rong, Lu Hua-Quan +2 more

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.

Acta Physica Sinica•Jan 1, 2006•1 citation

Phase transitions in a three-dimensional kinetic spin-1/2 Ising model with random field: Effective-field-theory study

Emanuel Costabile, J. Ricardo de Sousa

The dynamical phase transitions of the kinetic Ising model in the presence of a random magnetic field with a bimodal probability distribution is studied by using effective-field theory (EFT) with correlations. We have used a Glauber-type stochastic dynamic to describe the time evolution of the system, where the system strongly depends on the H≡√<H(i)(2)>(c) root mean square deviation of the magnetic field. The EFT dynamic equation is given for the simple cubic lattice (z=6), and the dynamic order parameter is calculated. The system presents ferromagnetic and paramagnetic states for low and high temperatures, respectively. Our results predict first-order transitions at low temperatures and large disorder strengths, which corresponds to the existence of a nonequilibrium tricritical point (TCP) in a phase diagram in the T-H plane. We compare the results with the equilibrium phase diagram, where only the first-order line is different. Our qualitative results are compatible with recent Monte Carlo simulations.

Physical Review E•Jan 13, 2012•15 citations

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

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

Shao Yuan-Zhi, Zhong Wei-Rong, Lin Guang-ming +1 more

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.

Acta Physica Sinica•Jan 1, 2004•3 citations
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. T TCP =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 H 0 , reduced temperature T / T C and the frequency ω as τ = C .ω α . H 0 −β .( T / T C ) −γ .
We systematically investigate the dynamical response of a three-dimensional kinetic isotropic Heisenberg spin system (HSS) to an external driving field by Monte Carlo numerical simulation. The dynamical response of the isotropic HSS differs obviously from those of the anisotropic Ising spin system in which no real stable ordered state and relevant dynamical phase transition were observed in the kinetic HSS. There is a threshold time after which the magnetization m ( t ) in the HSS driven by a symmetrical external field always tends asymptotically to a disorder state regardless of the initial state of the system. The threshold time depends on the reduced temperature T / T C of the investigated spin system, amplitude H 0 and frequency of the external field, i.e. τ = C ·ω α · H 0 -β ·( T / T C ) -γ . C is a constant equal to 0.0302 for a three-dimensional lattice and exponents α = 1.18±0.01, β = 1.81±0.01 and γ = 1.68±0.01.
The dynamic phase transition has been studied in the three-dimensional kinetic Ising model in the presence of a time-varying(sinusoidal)magnetic field by Monte Carlo simulation.The nature of the transition is characterized by studying the distribution of the order parameter.The system is in contact with an isothermal heat bath at temperature T.We varied the magnitude of the magnetic field,keeping the frequency of the magnetic field unchanged.For the lower values of the environment temperature the transition is discontinuous and it is continuous for higher values of the environment temperature,indicating the existence of a tricritical point (TCP) on the phase boundary.The TCP shifts towards higher temperature region with the decrease of frequency.i.e:TTCP=1.33×e(-ω/30.7)
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.
The dynamical phase transitions of the kinetic Ising model in the presence of a random magnetic field with a bimodal probability distribution is studied by using effective-field theory (EFT) with correlations. We have used a Glauber-type stochastic dynamic to describe the time evolution of the system, where the system strongly depends on the H≡√<H(i)(2)>(c) root mean square deviation of the magnetic field. The EFT dynamic equation is given for the simple cubic lattice (z=6), and the dynamic order parameter is calculated. The system presents ferromagnetic and paramagnetic states for low and high temperatures, respectively. Our results predict first-order transitions at low temperatures and large disorder strengths, which corresponds to the existence of a nonequilibrium tricritical point (TCP) in a phase diagram in the T-H plane. We compare the results with the equilibrium phase diagram, where only the first-order line is different. Our qualitative results are compatible with recent Monte Carlo simulations.
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.
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.