Spin, bond and global fluctuation-dissipation relations in the non-equilibrium spherical ferromagnet

Abstract

We study the out-of-equilibrium dynamics of the spherical ferromagnet after a quench to its critical temperature. We calculate correlation and response functions for spin observables which probe lengthscales much larger than the lattice spacing but smaller than the system size, and find that the asymptotic fluctuation-dissipation ratio (FDR) X^inf is the same as for local observables. This is consistent with our earlier results for the Ising model in dimension d=1 and d=2. We also check that bond observables, both local and long-range, give the same asymptotic FDR. In the second part of the paper the analysis is extended to global observables, which probe correlations among all N spins. Here non-Gaussian fluctuations arising from the spherical constraint need to be accounted for, and we develop a systematic expansion in 1/sqrt{N} to do this. Applying this to the global bond observable, i.e. the energy, we find that non-Gaussian corrections change its FDR to a nontrivial value which we calculate exactly for all dimensions d>2. Finally, we consider quenches from magnetized initial states. Here even the FDR for the global spin observable, i.e. the magnetization, is nontrivial. It differs from the one for unmagnetized states even in d>4, signalling the appearance of a distinct dynamical universality class of magnetized critical coarsening. For lower d the FDR is irrational even to first order in 4-d and d-2, the latter in contrast to recent results for the n-vector model.

arXiv comment58 pages, 5 figures

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• Dynamics of the directed Ising chain
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• Spherical model of growing interfaces
• Characterisation of non-equilibrium growth through global two-time quantities
• Slow dynamics in critical ferromagnetic vector models relaxing from a magnetized initial state
• Dynamic crossover in the global persistence at criticality
• Energy and Heat Fluctuations in a Temperature Quench
• Absence of logarithmic scaling in the ageing behaviour of the 4D spherical model
• Fluctuations and effective temperatures in coarsening
• The role of initial conditions in the ageing of the long-range spherical model
• Dynamic heterogeneities in critical coarsening: Exact results for correlation and response fluctuations in finite-sized spherical models (Version 2)
• Autocorrelation functions in phase-ordering kinetics from local scale-invariance
• Physical ageing from generalised time-translation-invariance
• Singular behavior of fluctuations in a relaxation process
• Non-equilibrium relaxations: ageing and finite-size effects
• Kinetics of phase-separation in the critical spherical model and local scale-invariance
• Aging and fluctuation-dissipation ratio in a nonequilibrium $q$-state lattice model
• Entropy-based characterizations of the observable-dependence of the fluctuation-dissipation temperature
• Fluctuation-dissipation relations in critical coarsening: crossover from unmagnetized to magnetized initial states
• Dynamic crossover in the persistence probability of manifolds at criticality