Nonlinear susceptibilities and the measurement of a cooperative length

Abstract

We derive the exact beyond-linear fluctuation dissipation relation, connecting the response of a generic observable to the appropriate correlation functions, for Markov systems. The relation, which takes a similar form for systems governed by a master equation or by a Langevin equation, can be derived to every order, in large generality with respect to the considered model, in equilibrium and out of equilibrium as well. On the basis of the fluctuation dissipation relation we propose a particular response function, namely the second order susceptibility of the two-particle correlation function, as an effective quantity to detect and quantify cooperative effects in glasses and disordered systems. We test this idea by numerical simulations of the Edwards-Anderson model in one and two dimensions.

5 pages, 2 figures

References in corpus (3)

• Effective critical behavior of the two-dimensional Ising spin glass with bimodal interactions
• Dynamical scaling in Ising and vector spin glasses
• Correlation Length of the Two-Dimensional Ising Spin Glass with Gaussian Interactions

Cited by in corpus (17)

• Temperature in and out of equilibrium: a review of concepts, tools and attempts
• Nonlinear response and fluctuation dissipation relations
• Microscopic theory for negative differential mobility in crowded environments
• Nonlinear response of inertial tracers in steady laminar flows: differential and absolute negative mobility
• Active matter under control: Insights from response theory
• Ageing at the Spin-Glass/Ferromagnet Transition: Monte Carlo Simulation using GPUs
• Anomalous force-velocity relation of driven inertial tracers in steady laminar flows
• Dynamic fluctuations in unfrustrated systems: random walks, scalar fields and the Kosterlitz-Thouless phase
• Measurement of second-order response without perturbation
• The Many Faces of Fluctuation-Dissipation Relations Out of Equilibrium
• Modeling non-linear dielectric susceptibilities of supercooled molecular liquids
• Effective temperatures for single particle system under dichotomous noise
• Growth Kinetics and Aging Phenomena in a Frustrated System
• Coarse-grained Second Order Response Theory
• Nonlinear Response Relations and Fluctuation-Response Inequalities for Nonequilibrium Stochastic Systems
• Effects of Frustration on Fluctuation-dissipation Relations
• Thermalization with a multibath: an investigation in simple models