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

Pasquale Calabrese·Andrea Gambassi
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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.

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Pasquale Calabrese, Andrea Gambassi. 2004-07-30. On the definition of a unique effective temperature for non-equilibrium critical systems. https://doi.org/10.1088/1742-5468%2F2004%2F07%2Fp07013

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