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29 March 2024
 
  » arxiv » cond-mat/0301493

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Fluctuation-dissipation relations in the non-equilibrium critical dynamics of Ising models
Peter Mayer ; Ludovic Berthier ; Juan P. Garrahan ; Peter Sollich ;
Date 24 Dec 2002
Journal Phys. Rev. E 68, 016116 (2003) DOI: 10.1103/PhysRevE.68.016116
Subject Statistical Mechanics; Disordered Systems and Neural Networks | cond-mat.stat-mech cond-mat.dis-nn
AbstractWe investigate the relation between two-time, multi-spin, correlation and response functions in the non-equilibrium critical dynamics of Ising models in d=1 and d=2 spatial dimensions. In these non-equilibrium situations, the fluctuation-dissipation theorem (FDT) is not satisfied. We find FDT `violations’ qualitatively similar to those reported in various glassy materials, but quantitatively dependent on the chosen observable, in contrast to the results obtained in infinite-range glass models. Nevertheless, all FDT violations can be understood by considering separately the contributions from large wavevectors, which are at quasi-equilibrium and obey FDT, and from small wavevectors where a generalized FDT holds with a non-trivial limit fluctuation-dissipation ratio X. In d=1, we get X = 1/2 for spin observables, which measure the orientation of domains, while X = 0 for observables that are sensitive to the domain-wall motion. Numerical simulations in d=2 reveal a unique X = 0.34 for all observables. Measurement protocols for X are discussed in detail. Our results suggest that the definition of an effective temperature Teff = T / X for large length scales is generically possible in non-equilibrium critical dynamics.
Source arXiv, cond-mat/0301493
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