Fluctuations of two-time quantities and non-linear response functions

Abstract

We study the fluctuations of the autocorrelation and autoresponse functions and, in particular, their variances and co-variance. In a first general part of the Article, we show the equivalence of the variance of the response function with the second-order susceptibility of a composite operator, and we derive an equilibrium fluctuation-dissipation theorem beyond-linear order relating it to the other variances. In a second part of the paper we apply the formalism to the study to non-disordered ferromagnets, in equilibrium or in the coarsening kinetics following a critical or sub-critical quench. We show numerically that the variances and the non-linear susceptibility obey scaling with respect to the coherence length $\xi$ in equilibrium, and with respect to the growing length $L(t)$ after a quench, similarly to what is known for the autocorrelation and the autoresponse functions.

21 pages, 5 figures. To appear on Jstat

References in corpus (17)

• Fluctuations and response of nonequilibrium states
• Fluctuation-dissipation relations in the non-equilibrium critical dynamics of Ising models
• Nonlinear response and fluctuation dissipation relations
• Efficient measurement of linear susceptibilities in molecular simulations: Application to aging supercooled liquids
• Fluctuations in glassy systems
• Scaling of the linear response in simple ageing systems without disorder
• Bona Fide Thermodynamic Temperature in Nonequilibrium Kinetic Ising Models
• Nonlinear susceptibilities and the measurement of a cooperative length
• On universality in aging ferromagnets
• Scaling and super-universality in the coarsening dynamics of the 3d random field Ising model
• Fluctuation-dissipation relations and field-free algorithms for the computation of response functions
• Phase-ordering kinetics on graphs
• Generic features of the fluctuation dissipation relation in coarsening systems
• Aging dynamics and the topology of inhomogenous networks
• Dynamic Heterogeneity in the Glauber-Ising chain
• Dynamic heterogeneities in critical coarsening: Exact results for correlation and response fluctuations in finite-sized spherical models (Version 2)
• Phase ordering and universality for continuous symmetry models on graphs

Cited by in corpus (6)

• How soon after a zero-temperature quench is the fate of the Ising model sealed?
• On anomalous diffusion and the out of equilibrium response function in one-dimensional models
• Dynamic fluctuations in unfrustrated systems: random walks, scalar fields and the Kosterlitz-Thouless phase
• Fluctuations of two-time quantities and time-reparametrization invariance in spin-glasses
• Identification of the critical temperature from non-equilibrium time-dependent quantities
• Susceptibility of quasiclassical Brownian motion in harmonic nonlinear potentials