2004/06/30 by Pasquale Calabrese, Andrea Gambassi · 157 citations
Mathematics · Physics and Astronomy · #Class (philosophy) #Computation #Critical exponent #Critical point (mathematics) #Gaussian #Limit (mathematics) #Observable #Quadratic equation #Quantum many-body systems #Scaling #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1088/1742-5468/2004/07/p07013
published in Journal of Statistical Mechanics Theory and Experiment 2004(07), P07013 (Institute of Physics) · 32 pages, 5 figures. Minor changes, published version
arxiv created 2004/07/30 · openalex publication_date 2004/07/31 · arxiv updated 2011/02/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider the problem of the definition of an effective temperature via the long-time limit of the fluctuation-dissipation ratio 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 , 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 -expansion for two quadratic observables. This implies that, contrarily to what is often conjectured, a unique effective temperature cannot be defined for this class of models.