Nonequilibrium critical dynamics of ferromagnetic spin systems

Abstract

We use simple models (the Ising model in one and two dimensions, and the spherical model in arbitrary dimension) to put to the test some recent ideas on the slow dynamics of nonequilibrium systems. In this review the focus is on the temporal evolution of two-time quantities and on the violation of the fluctuation-dissipation theorem, with special emphasis given to nonequilibrium critical dynamics.

11 pages, 2 figures.Contribution to the Proceedings of the ESF SPHINX meeting `Glassy behaviour of kinetically constrained models' (Barcelona, March 22-25, 2001). To appear in a special issue of J. Phys. Cond. Matt

References in corpus (2)

• Nonequilibrium Critical Dynamics of the 2D XY model
• Aging, phase ordering and conformal invariance

Cited by in corpus (104)

• Glassy dynamics of kinetically constrained models
• Violation of the fluctuation-dissipation theorem in glassy systems: basic notions and the numerical evidence
• Ageing Properties of Critical Systems
• Phenomenology of local scale invariance: from conformal invariance to dynamical scaling
• Schr"odinger invariance and space-time symmetries
• On the definition of a unique effective temperature for non-equilibrium critical systems
• A far-from-equilibrium fluctuation-dissipation relation for an Ising-Glauber-like model
• Local scale-invariance and ageing in noisy systems
• Aging and coarsening in isolated quantum systems after a quench: exact results for the quantum $O(N)$ model with $N\to \infty$
• Response of non-equilibrium systems with long-range initial correlations
• Fluctuation-dissipation relations and effective temperatures in simple non-mean field systems
• Two-time autocorrelation function in phase-ordering kinetics from local scale-invariance
• Local scale invariance as dynamical space-time symmetry in phase-ordering kinetics
• Ageing in disordered magnets and local scale-invariance
• Scaling of the linear response in simple ageing systems without disorder
• From urn models to zero-range processes: statics and dynamics
• Superuniversality in phase-ordering disordered ferromagnets
• Nonequilibrium critical dynamics of the ferromagnetic Ising model with Kawasaki dynamics
• Critical aging of Ising ferromagnets relaxing from an ordered state
• Ageing phenomena without detailed balance: the contact process
• Scaling of the magnetic linear response in phase-ordering kinetics
• Universal aging properties at a disordered critical point
• Fluctuations in the coarsening dynamics of the O(N) model: are they similar to those in glassy systems?
• On the universality of the fluctuation-dissipation ratio in non-equilibrium critical dynamics
• Corrections to local scale invariance in the non-equilibrium dynamics of critical systems: numerical evidences
• Aging phenomena in critical semi-infinite systems
• Langevin simulations of the out-of-equilibrium dynamics of the vortex glass in high-temperature superconductors
• Effective temperature in the quench of coarsening systems to and below $T_C$
• Scaling and universality in the aging kinetics of the two-dimensional clock model
• Ageing in the critical contact process: a Monte Carlo study
• Dynamical symmetries of semi-linear Schrödinger and diffusion equations
• Aging in the glass phase of a 2D random periodic elastic system
• Dynamics of the directed Ising chain
• Dynamic critical behaviour in Ising spin glasses
• Ageing, dynamical scaling and its extensions in many-particle systems without detailed balance
• Out-of-equilibrium critical dynamics at surfaces: Cluster dissolution and non-algebraic correlations
• Spherical model of growing interfaces
• Ageing in the contact process: Scaling behavior and universal features
• Kinetics of the long-range spherical model
• Ageing and dynamical scaling in the critical Ising spin glass
• On non-local representations of the ageing algebra
• Schrödinger symmetry: a historical review
• Nonequilibrium critical dynamics in inhomogeneous systems
• Nonequilibrium critical dynamics with domain wall and surface
• Lindblad dynamics of a quantum spherical spin
• Universality of Fluctuation-Dissipation Ratios: The Ferromagnetic Model
• Slow dynamics in critical ferromagnetic vector models relaxing from a magnetized initial state
• Dynamical off-equilibrium scaling across magnetic first-order phase transitions
• Dynamic fluctuations in unfrustrated systems: random walks, scalar fields and the Kosterlitz-Thouless phase
• The kinetic spherical model in a magnetic field
• Out-of-equilibrium properties of the semi-infinite kinetic spherical model
• Development and regression of a large fluctuation
• Exact two-time correlation and response functions in the one-dimensional coagulation-diffusion process by the empty-interval-particle method
• Out of equilibrium dynamics of the spiral model
• Exact correlations in the one-dimensional coagulation-diffusion process by the empty-interval method
• Non-equilibrium critical dynamics in disordered ferromagnets
• Absence of logarithmic scaling in the ageing behaviour of the 4D spherical model
• On the scaling and ageing behaviour of the alternating susceptibility in spin glasses and local scale-invariance
• Short-time critical dynamics at perfect and non-perfect surface
• Coarsening dynamics of zero-range processes
• Freezing in stripe states for kinetic Ising models: a comparative study of three dynamics
• Dynamics of the two-dimensional directed Ising model in the paramagnetic phase
• Comment on "Fluctuation-dissipation relations in the nonequilibrium critical dynamics of Ising models"
• Ageing in bosonic particle-reaction models with long-range transport
• Universal late-time dynamics in isolated one-dimensional statistical systems with topological excitations
• Fluctuations and effective temperatures in coarsening
• Autocorrelation functions in phase-ordering kinetics from local scale-invariance
• Physical ageing from generalised time-translation-invariance
• Universality in three-dimensional Ising spin glasses: Nonequilibrium dynamics from Monte Carlo simulations
• The non-equilibrium response of the critical Ising model: Universal scaling properties and Local Scale Invariance
• Dynamics of the two-dimensional directed Ising model: zero-temperature coarsening
• Asymmetric Langevin dynamics for the ferromagnetic spherical model
• Kinetics of phase-separation in the critical spherical model and local scale-invariance
• Observable Dependent Quasi-Equilibrium in Slow Dynamics
• Non-markovian global persistence in phase-ordering kinetics
• Fluctuations of two-time quantities and non-linear response functions
• Dynamics of systems with isotropic competing interactions in an external field: a Langevin approach
• Logarithmic corrections in the aging of the fully-frustrated Ising model
• Competition between dynamic and thermal relaxation in non-equilibrium spin systems above the critical point
• Local aging phenomena close to magnetic surfaces
• Collective non-equilibrium dynamics at surfaces and the spatio-temporal edge
• Nonequilibrium critical dynamics of the two-dimensional $\pm J$ Ising model
• Non-equilibrium critical properties of the Ising model on product graphs
• Nonequilibrium critical dynamics of the three-dimensional gauge glass
• Ultralocal nature of geometrogenesis
• Transfer operator analysis of the parallel dynamics of disordered Ising chains
• Growth Kinetics and Aging Phenomena in a Frustrated System
• Lie symmetries of semi-linear Schrödinger equations and applications
• Reentrance during nonequilibrium relaxation
• Critical behavior of spin and chiral degrees of freedom in three-dimensional disordered XY models studied by the nonequilibrium aging method
• Theory of Critical Phenomena with Long-Range Temporal Interaction
• Correlators in phase-ordering from Schrödinger-invariance
• Nonequilibrium dynamics of fully frustrated Ising models at T=0
• Critical ageing correlators from Schrödinger-invariance
• Nonequilibrium critical dynamics of the two-dimensional Ising model quenched from a correlated initial state
• Slow relaxation in microcanonical warming of a Ising lattice
• Aging and stationary properties of non-equilibrium symmetrical three-state models
• Effects of Frustration on Fluctuation-dissipation Relations
• Ageing without detailed balance: local scale invariance applied to two exactly solvable models
• Short-time dynamics in phase-ordering kinetics
• Dynamic relaxation of topological defect at Kosterlitz-Thouless phase transition
• Dynamical critical behavior on the Nishimori point of frustrated Ising models
• Dynamical space-time symmetry for ageing far from equilibrium
• Schrödinger-invariance in the voter model