On the connection between off-equilibrium response and statics in non disordered coarsening systems

Abstract

The connection between the out of equilibrium linear response function and static properties established by Franz, Mezard, Parisi and Peliti for slowly relaxing systems is analyzed in the context of phase ordering processes. Separating the response in the bulk of domains from interface response, we find that in order for the connection to hold the interface contribution must be asymptotically negligible. How fast this happens depends on the competition between interface curvature and the perturbing external field in driving domain growth. This competition depends on space dimensionality and there exists a critical value $d_c=3$ below which the interface response becomes increasingly important eventually invalidating the connection between statics and dynamics as the limit $d=1$ is reached. This mechanism is analyzed numerically for the Ising model with $d$ ranging from 1 to 4 and analytically for a continuous spin model with arbitrary dimensionality.

20 pages, 9 figures. European Physical Journal B, to appear

Cited by in corpus (51)

• Ageing Properties of Critical Systems
• Off-equilibrium generalization of the fluctuation dissipation theorem for Ising spins and measurement of the linear response function
• Spatially heterogeneous ages in glassy dynamics
• Nonlinear response and fluctuation dissipation relations
• Fluctuation-dissipation relations in the non-equilibrium critical dynamics of Ising models
• Crossover in Growth Law and Violation of Superuniversality in the Random Field Ising Model
• Slow relaxation in the large N model for phase ordering
• Ageing in disordered magnets and local scale-invariance
• Local scale invariance as dynamical space-time symmetry in phase-ordering kinetics
• Scaling of the linear response function from zero field cooled and thermoremanent magnetization in phase ordering kinetics
• Fluctuation-Dissipation relations far from Equilibrium
• Scaling of the linear response in simple ageing systems without disorder
• Growth Law and Superuniversality in the Coarsening of Disordered Ferromagnets
• Scaling Behavior of Response Functions in the Coarsening Dynamics of Disordered Ferromagnets
• Scaling of the magnetic linear response in phase-ordering kinetics
• Response Functions in Phase Ordering Kinetics
• Fluctuation-dissipation relations and field-free algorithms for the computation of response functions
• Influence of thermal fluctuations on the geometry of the interfaces of the quenched Ising model
• 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
• Phase-ordering kinetics on graphs
• Generic features of the fluctuation dissipation relation in coarsening systems
• Scaling in the Aging Dynamics of the Site-diluted Ising Model
• Correction to scaling in the response function of the 2d kinetic Ising model
• Relaxation and overlap probability function in the spherical and mean spherical model
• Test of Local Scale Invariance from the direct measurement of the response function in the Ising model quenched to and to below $T_C$
• Comment on "Aging, phase ordering and conformal invariance"
• Dynamics of the directed Ising chain
• Aging dynamics and the topology of inhomogenous networks
• Universality of the off-equilibrium response function in the kinetic Ising chain
• Correlation Functions and Fluctuation-Dissipation Relation in Driven Mixtures: an exactly solvable model
• The fluctuation-dissipation relation in an Ising model without detailed balance
• The role of initial state and final quench temperature on the aging properties in phase-ordering kinetics
• Fluctuations and effective temperatures in coarsening
• Effects of an external drive on the fluctuation-dissipation relation of phase-ordering systems
• Topological regulation of activation barriers on fractal substrates
• Phase ordering in disordered and inhomogeneous systems
• Comment on "Scaling of the linear response in simple aging systems without disorder"
• Reply to "Comment on 'Scaling of the linear response in simple ageing systems without disorder' "
• Phase ordering and universality for continuous symmetry models on graphs
• The non-equilibrium response of the critical Ising model: Universal scaling properties and Local Scale Invariance
• Fluctuations of two-time quantities and non-linear response functions
• Non-equilibrium critical properties of the Ising model on product graphs
• Heat exchanges in coarsening systems
• Condensation and equilibration in an urn model
• Growth Kinetics and Aging Phenomena in a Frustrated System
• Non trivial behavior of the linear response function in phase ordering kinetics
• Equilibrium structure and off-equilibrium kinetics of a magnet with tunable frustration
• On a relation between roughening and coarsening
• Effects of Frustration on Fluctuation-dissipation Relations
• Thermalization with a multibath: an investigation in simple models