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

Canadian Journal of Physics

Kinetic Ising model on alternating linear chains

L.L. Gonçalves, N. T. de Oliveira

Published Sep 1, 1985• 5 citations
Publisher

Abstract

The kinetic Ising model on two alternating linear chains is considered. Exact expressions are obtained for the wave-vector frequency-dependent susceptibility and the time evolution of the magnetization. It is shown that the long-time behaviour of the magnetization in both systems is identical to the one in the uniform chain. Although they behave similarly as far as the relaxation of the magnetization is concerned, they have different dynamic magnetic responses at equilibrium. It is also shown that at T = 0 for a given set of parameters the static susceptibility diverges at a well-defined wave vector, which is a consequence of the ordering of the ground state.

DOI
10.1139/p85-199

Related papers

Nagel scaling, relaxation and universality in the kinetic Ising model in an alternating isotopic chain

L.L. Gonçalves, M. López de Haro, J. Tagüeña-Martı́nez +1 more

The dynamic critical exponent and the frequency and wave-vector dependent susceptibility of the kinetic Ising model with Glauber dynamics on an alternating isotopic chain are examined. The analysis provides to our knowledge the first connection between a microscopic model and the Nagel scaling curve originally proposed to describe dielectric susceptibility measurements of several glass-forming liquids. While support is given to the hypothesis relating the Nagel scaling to multiple relaxation processes, it is also found that the scaling function may also exhibit plateau regions and does not hold for low temperatures.

arXiv:cond-mat/9911225•Nov 15, 1999•1 citation

Nagel Scaling, Relaxation, and Universality in the Kinetic Ising Model on an Alternating Isotopic Chain

L.L. Gonçalves, M. López de Haro, J. Tagüeña-Martı́nez +1 more

The dynamic critical exponent and the frequency and wave-vector dependent susceptibility of the kinetic Ising model on an alternating isotopic chain with Glauber dynamics are examined. The analysis provides a connection between a microscopic model and the Nagel scaling curve originally proposed to describe dielectric susceptibility measurements of several glass-forming liquids. While support is given to the hypothesis relating the Nagel scaling to multiple relaxation processes, it is also found that the scaling function may exhibit plateau regions and does not hold for all temperatures.

Physical Review Letters•Feb 14, 2000•6 citations

Dynamical Nature of the Phase Transition of the Two-Dimensional Kinetic Ising Model

Seiji Miyashita, Hiroshi Takano

We study dynamic properties of the critical phenomena of the two-dimensional kinetic Ising model above and below the critical temperature Tc. In particular, we study the critical slowing-down (T > Tc) and the symmetry breaking (T ≪ Tc) through the temperature- and size-dependences of relaxation time of magnetization and we compare the dependences with those of static quantities such as the susceptibility. We find intrinsic dynamical critical behaviour on both sides of Tc with a critical region as wide as the one in the static critical behaviour. We also discuss the dynamic properties as an eigenvalue problem of the time-evolution operator (the Liouville operator) and thier scaling properties.

Progress of Theoretical Physics•May 1, 1985•65 citations

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

Muktish Acharyya

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.

arXiv:1010.4366•Physica Scripta•Sep 1, 2011•10 citations

Non-equilibrium critical dynamics of the ferromagnetic Ising model with Kawasaki dynamics

Claude Godrèche, Florent Krzaka a, Federico Ricci‐Tersenghi

We investigate the temporal evolution of a ferromagnetic system of Ising spins evolving under Kawasaki dynamics from a random initial condition, in spatial dimensions one and two. We examine in detail the asymptotic behaviour of the two-time correlation and response functions. The linear response is measured without applying a field, using a recently proposed algorithm. For the chain at vanishingly small temperature, we introduce an accelerated dynamics which has the virtue of projecting the system into the asymptotic scaling regime. This allows us to revisit critically previous works on the behaviour at large time of the two-time autocorrelation and response functions. We also analyse the case of the two-dimensional system at criticality. A comparison with Glauber dynamics is performed in both dimensionalities, in order to underline the similarities and differences in the phenomenology of the two dynamics.

arXiv:cond-mat/0401334•Journal of Statistical Mechanics Theory and Experiment•May 1, 2004•41 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
The kinetic Ising model on two alternating linear chains is considered. Exact expressions are obtained for the wave-vector frequency-dependent susceptibility and the time evolution of the magnetization. It is shown that the long-time behaviour of the magnetization in both systems is identical to the one in the uniform chain. Although they behave similarly as far as the relaxation of the magnetization is concerned, they have different dynamic magnetic responses at equilibrium. It is also shown that at T = 0 for a given set of parameters the static susceptibility diverges at a well-defined wave vector, which is a consequence of the ordering of the ground state.
The dynamic critical exponent and the frequency and wave-vector dependent susceptibility of the kinetic Ising model with Glauber dynamics on an alternating isotopic chain are examined. The analysis provides to our knowledge the first connection between a microscopic model and the Nagel scaling curve originally proposed to describe dielectric susceptibility measurements of several glass-forming liquids. While support is given to the hypothesis relating the Nagel scaling to multiple relaxation processes, it is also found that the scaling function may also exhibit plateau regions and does not hold for low temperatures.
The dynamic critical exponent and the frequency and wave-vector dependent susceptibility of the kinetic Ising model on an alternating isotopic chain with Glauber dynamics are examined. The analysis provides a connection between a microscopic model and the Nagel scaling curve originally proposed to describe dielectric susceptibility measurements of several glass-forming liquids. While support is given to the hypothesis relating the Nagel scaling to multiple relaxation processes, it is also found that the scaling function may exhibit plateau regions and does not hold for all temperatures.
We study dynamic properties of the critical phenomena of the two-dimensional kinetic Ising model above and below the critical temperature Tc. In particular, we study the critical slowing-down (T > Tc) and the symmetry breaking (T ≪ Tc) through the temperature- and size-dependences of relaxation time of magnetization and we compare the dependences with those of static quantities such as the susceptibility. We find intrinsic dynamical critical behaviour on both sides of Tc with a critical region as wide as the one in the static critical behaviour. We also discuss the dynamic properties as an eigenvalue problem of the time-evolution operator (the Liouville operator) and thier scaling properties.
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.
We investigate the temporal evolution of a ferromagnetic system of Ising spins evolving under Kawasaki dynamics from a random initial condition, in spatial dimensions one and two. We examine in detail the asymptotic behaviour of the two-time correlation and response functions. The linear response is measured without applying a field, using a recently proposed algorithm. For the chain at vanishingly small temperature, we introduce an accelerated dynamics which has the virtue of projecting the system into the asymptotic scaling regime. This allows us to revisit critically previous works on the behaviour at large time of the two-time autocorrelation and response functions. We also analyse the case of the two-dimensional system at criticality. A comparison with Glauber dynamics is performed in both dimensionalities, in order to underline the similarities and differences in the phenomenology of the two dynamics.
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).