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

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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 length scales much larger than the lattice spacing but smaller than the system size, and find that the asymptotic fluctuation-dissipation ratio (FDR) X-infinity is the same as for local observables. This is consistent with our earlier results for the Ising model in dimension d = 1and 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/root 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 dynmical 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 transverse FDR in the n-vector model
Original languageEnglish
Pages (from-to)2853 - 2907
Number of pages55
JournalJOURNAL OF PHYSICS A MATHEMATICAL AND GENERAL
Volume39
Issue number12
DOIs
Publication statusPublished - 24 Mar 2006

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