Response of non-equilibrium systems with long-range initial correlations

Abstract

The long-time dynamics of the $d$-dimensional spherical model with a non-conserved order parameter and quenched from an initial state with long-range correlations is studied through the exact calculation of the two-time autocorrelation and autoresponse functions. In the aging regime, these are given in terms of non-trivial universal scaling functions of both time variables. At criticality, five distinct types of aging are found, depending on the form of the initial correlations, while at low temperatures only a single type of aging exists. The autocorrelation and autoreponse exponents are shown to be generically different and to depend on the initial conditions. The scaling form of the two-time response functions agrees with a recent prediction coming from local scale invariance.

Latex, 18pp, 2 figures (final version)

References in corpus (2)

• Nonequilibrium critical dynamics of ferromagnetic spin systems
• Aging, phase ordering and conformal invariance

Cited by in corpus (58)

• 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
• Spatially heterogeneous ages in glassy dynamics
• Local scale-invariance and ageing in noisy systems
• The non-equilibrium phase transition of the pair-contact process with diffusion
• Two-loop Critical Fluctuation-Dissipation Ratio for the Relaxational Dynamics of the O(N) Landau-Ginzburg Hamiltonian
• 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
• Aging and fluctuation-dissipation ratio for the diluted Ising Model
• Scaling of the linear response in simple ageing systems without disorder
• Nonequilibrium critical dynamics of the ferromagnetic Ising model with Kawasaki dynamics
• Critical aging of Ising ferromagnets relaxing from an ordered state
• Aging in coarsening diluted ferromagnets
• 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
• Exact multilocal renormalization on the effective action : application to the random sine Gordon model statics and non-equilibrium dynamics
• Aging phenomena in critical semi-infinite systems
• Aging at Criticality in Model C Dynamics
• Ageing in the critical contact process: a Monte Carlo study
• Dynamical symmetries of semi-linear Schrödinger and diffusion equations
• Critical aging of a ferromagnetic system from a completely ordered state
• Spin, bond and global fluctuation-dissipation relations in the non-equilibrium spherical ferromagnet
• Aging in the glass phase of a 2D random periodic elastic system
• Ageing, dynamical scaling and its extensions in many-particle systems without detailed balance
• Spherical model of growing interfaces
• Ageing and dynamical scaling in the critical Ising spin glass
• Universality of Fluctuation-Dissipation Ratios: The Ferromagnetic Model
• Local scale invariance in the parity conserving nonequilibrium kinetic Ising model
• Slow dynamics in critical ferromagnetic vector models relaxing from a magnetized initial state
• The kinetic spherical model in a magnetic field
• Out-of-equilibrium properties of the semi-infinite kinetic spherical model
• Axiomatic construction of quantum Langevin equations
• Non-equilibrium critical dynamics in disordered ferromagnets
• Lindblad dynamics of the quantum spherical model
• On the scaling and ageing behaviour of the alternating susceptibility in spin glasses and local scale-invariance
• The role of initial conditions in the ageing of the long-range spherical model
• Autocorrelation functions in phase-ordering kinetics from local scale-invariance
• Physical ageing from generalised time-translation-invariance
• Non-equilibrium relaxations: ageing and finite-size effects
• Exactly solvable models of growing interfaces and lattice gases: the Arcetri models, ageing and logarithmic sub-ageing
• Asymmetric Langevin dynamics for the ferromagnetic spherical model
• Local aging phenomena close to magnetic surfaces
• Competition between dynamic and thermal relaxation in non-equilibrium spin systems above the critical point
• Quantum dynamics far from equilibrium: a case study in the spherical model
• Dynamical symmetries in the non-equilibrium dynamics of the directed spherical model
• Reentrance during nonequilibrium relaxation
• Correlators in phase-ordering from Schrödinger-invariance
• Nonequilibrium critical dynamics of the two-dimensional Ising model quenched from a correlated initial state
• Ageing, dynamical scaling and conformal invariance
• Non-equilibrium dynamics of the open quantum $O(n)$-model with non-Markovian noise: exact results
• Dynamical space-time symmetry for ageing far from equilibrium
• Schrödinger-invariance in the voter model