Nonlinear response and fluctuation dissipation relations

TL;DR

This paper derives a unified framework for off-equilibrium fluctuation dissipation relations (FDR) applicable to Ising and continuous spins, enabling efficient numerical response function computation and exploring effective temperature in glassy and coarsening systems.

Contribution

It provides a general derivation of nonlinear FDR for Markovian spin systems and demonstrates their applications in probing cooperative length scales and defining effective temperatures.

Findings

Second order FDR effectively probes cooperative length scales in glassy systems.

Effective temperature from nonlinear FDR matches linear FDR in coarsening systems.

Zero field algorithms improve numerical response function calculations.

Abstract

A unified derivation of the off equilibrium fluctuation dissipation relations (FDR) is given for Ising and continous spins to arbitrary order, within the framework of Markovian stochastic dynamics. Knowledge of the FDR allows to develop zero field algorithms for the efficient numerical computation of the response functions. Two applications are presented. In the first one, the problem of probing for the existence of a growing cooperative length scale is considered in those cases, like in glassy systems, where the linear FDR is of no use. The effectiveness of an appropriate second order FDR is illustrated in the test case of the Edwards-Anderson spin glass in one and two dimensions. In the second one, the important problem of the definition of an off equilibrium effective temperature through the nonlinear FDR is considered. It is shown that, in the case of coarsening systems, the effective temperature derived from the second order FDR is consistent with the one obtained from the linear FDR.