Slow dynamics in critical ferromagnetic vector models relaxing from a magnetized initial state

Abstract

Within the universality class of ferromagnetic vector models with O(n) symmetry and purely dissipative dynamics, we study the non-equilibrium critical relaxation from a magnetized initial state. Transverse correlation and response functions are exactly computed for Gaussian fluctuations and in the limit of infinite number n of components of the order parameter. We find that the fluctuation-dissipation ratios (FDRs) for longitudinal and transverse modes differ already at the Gaussian level. In these two exactly solvable cases we completely describe the crossover from the short-time to the long-time behavior, corresponding to a disordered and a magnetized initial condition, respectively. The effects of non-Gaussian fluctuations on longitudinal and transverse quantities are calculated in the first order in the epsilon-expansion and reliable three-dimensional estimates of the two FDRs are obtained.

41 pages, 9 figures

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• The role of initial conditions in the ageing of the long-range spherical model
• Decoherence of Bell states by local interactions with a suddenly quenched spin environment
• Aging and fluctuation-dissipation ratio in a nonequilibrium $q$-state lattice model
• Universal amplitudes ratios for critical aging via functional renormalization group
• Non-equilibrium dynamics of the open quantum $O(n)$-model with non-Markovian noise: exact results