Laboratoire de Physique des Materiaux,

Universite Henri Poincare Nancy I

B.P. 239, F - 54506 Vandoeuvre les Nancy Cedex,

FRANCE

E-mail: henkel@lpm.u-nancy.fr

**Dynamical space-time symmetry for ageing far from equilibrium**

**Abstract:**

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.

**References:**

- M. Henkel, Nucl. Phys. B641, 405 (2002); hep-th/0205256.
- M. Henkel and J. Unterberger, Nucl. Phys. B (in press); hep-th/0302187.
- M. Henkel and M. Pleimling, cond-mat/0302482.