In this thesis we study the out-of-equilibrium, critical dynamics of an exactly solvable model: the spherical ferromagnet. The use of ﬂuctuation-dissipation relations (FDR) has proved in recent years to be very fruitful to quantify the out-of-equilibrium dynamics of glassy systems and other systems exhibiting aging. A matter of recent intense debate has been wether the FDR can be interpreted in terms of an eﬀective temperature in non idealized long-ranged systems. Minimal requirements to pursue this interpretation are the existence of a limiting FD plot and the independence of the FDR on the particular observables chosen. The ﬁrst part of this thesis addresses the observable dependence of the asymptotic FDR. Correlation and response are calculated for spin and bond observables which probe lengthscales much larger than the lattice spacing but smaller than the system size and the resulting asymptotic FDR is shown to be the same as for local observables. Then the analysis is extended to observables which probe correlations among all the spins, where non-Gaussian ﬂuctuations arising from the spherical constraint need to be accounted for. These are found to change the FDR to a non trivial value which is calculated exactly for all dimensions d > 2. The second part of the thesis focuses on another interesting theoretical issue, i.e. the dependence of the asymptotic FDR on the initial conditions. For magnetized initial states one has to account for non-Gaussian eﬀects even for the global spin observable and the results show that the FDR for magnetized initial conditions falls within a diﬀerent universality class than the unmagnetized one. The eﬀect of a nonzero initial magnetization is explored further by looking at it as introducing a new timescale in the system and the crossover between the unmagnetized and the magnetized case is studied. Finally, dynamical heterogeneities are investigated by monitoring the ﬂuctuations of local two-time functions around their global average and the joint distribution of correlation and reponse around the global FD plot is explored.
|Date of Award||1 Oct 2007|
|Supervisor||Peter Sollich (Supervisor)|