Universality of Fluctuation-Dissipation Ratios: The Ferromagnetic Model

TL;DR

This paper analytically calculates the fluctuation-dissipation ratio (FDR) for Ising ferromagnets quenched to criticality, revealing two classes of critical coarsening dynamics depending on initial magnetization, with implications for defining effective temperatures.

Contribution

It provides an exact analytical solution for the FDR in long-range and short-range ferromagnetic models, distinguishing different dynamical classes based on initial conditions.

Findings

FDR equals 1/2 for unmagnetized systems

FDR equals 4/5 for systems with non-zero initial magnetization

Global observables are more reliable for detecting non-equilibrium FDRs

Abstract

We calculate analytically the fluctuation-dissipation ratio (FDR) for Ising ferromagnets quenched to criticality, both for the long-range model and its short-range analogue in the limit of large dimension. Our exact solution shows that, for both models, $X^\infty=1/2$ if the system is unmagnetized while $X^\infty=4/5$ if the initial magnetization is non-zero. This indicates that two different classes of critical coarsening dynamics need to be distinguished depending on the initial conditions, each with its own nontrivial FDR. We also analyze the dependence of the FDR on whether local and global observables are used. These results clarify how a proper local FDR (and the corresponding effective temperature) should be defined in long-range models in order to avoid spurious inconsistencies and maintain the expected correspondence between local and global results; global observables turn out to be far more robust tools for detecting non-equilibrium FDRs.