Dynamical space-time symmetry for ageing far from equilibrium
Ageing is a common phenomenon which occurs for example in ferromagnets quenched to a temperature below the critical temperature. It is characterized by the absence of time-translation invariance and the occurrence of dynamical scaling. We have suggested that this dynamical scaling can be generalized towards a local scale invariance under space-time dependent scale transformations. Indeed, infinitesimal local scale transformations can be constructed for any given value of the dynamical exponent z. They act as dynamical symmetries of certain non-local free-field equations.
The simplest case occurs for z=2. Is was thought that the relevant group is the Schroedinger group Sch_d, which is the maximal kinematic invariance group of the free Schroedinger equation with fixed mass. Treating the mass as an additional variable, we obtain an embedding of Sch_d into the complexified conformal group in d+2 dimensions. Besides a geometric understanding of the Schroedinger group, the classification of the parabolic subalgebras allows to identify dynamic symmetry algebras for the description of physical ageing processes. Explicit predictions for the response functions are obtained and tested in kinetic spin systems such as the Ising model with Glauber dynamics.