Nonlinear susceptibilities and the measurement of a cooperative length

Details Nonlinear susceptibilities and the measurement of a cooperative length Nonlinear susceptibilities and the measurement of a cooperative length

2008-05-22

arxiv.org/abs/0805.3457v1

Phys. Rev. B 77, 212201 (2008)

Physics

Condensed Matter

Statistical Mechanics

5 pages, 2 figures

Scientific paper

10.1103/PhysRevB.77.212201

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.

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