On the definition of a unique effective temperature for non-equilibrium critical systems

TL;DR

This paper investigates the possibility of defining a unique effective temperature in non-equilibrium critical systems, showing that fluctuations beyond Gaussian approximation prevent such a definition.

Contribution

It demonstrates that a unique effective temperature can be defined within Gaussian approximation but not when fluctuations are included beyond that, challenging previous conjectures.

Findings

Gaussian approximation yields a unique FDR for all local observables

Beyond Gaussian approximation, different observables have different FDRs

A first-order epsilon-expansion shows no universal effective temperature

Abstract

We consider the problem of the definition of an effective temperature via the long-time limit of the fluctuation-dissipation ratio (FDR) after a quench from the disordered state to the critical point of an O(N) model with dissipative dynamics. The scaling forms of the response and correlation functions of a generic observable are derived from the solutions of the corresponding Renormalization Group equations. We show that within the Gaussian approximation all the local observables have the same FDR, allowing for a definition of a unique effective temperature. This is no longer the case when fluctuations are taken into account beyond that approximation, as shown by a computation up to the first order in the epsilon-expansion for two quadratic observables. This implies that, contrarily to what often conjectured, a unique effective temperature can not be defined for this class of models.