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Dynamics through phase transitions

Sub-critical coarsening is the process whereby a macroscopic system in contact with an equilibrium reservoir orders after a rapid change in a parameter that takes it from a disordered phase into an ordered one in its equilibrium phase diagram. Closely related is critical coarsening, the process whereby a critical state is approached by quenching a disordered system right to the critical point.
One of our goals is to characterize the geometry of coarsening phenomena in distribution. We studied analytically the statistical and geometric properties of ordered structures in planar curvature driven coarsening. The results provide the first analytic proof of dynamic scaling in more than one dimension for a finite dimensional order parameter. We studied numerically 2d phase separation, domain growth
in the random bond ferromagnetic Ising model and the Potts model. Experiments in a liquid crystal -film confirmed our predictions and demonstrated that monitoring the time-evolution of structures can be a very efficient way to determine the dynamic universality class. More recently, we analyzed these same questions after a quench to a critical point. We studied the relaxation of the 2d kinetically constrained spiral model. We showed that any unblocked state de-correlates in -finite times in the full phase diagram and we proved that the dynamics occur via coarsening of vacancy lines.
Quenches at very slow rates attracted a lot of attention in the cosmology and the condensed matter communities. A proposal for the cooling-rate dependence is given by the Kibble-Zurek (KZ) mechanism. We revisited these ideas in phase ordering systems across a second order phase transition and we revealed the limitations of the KZ mechanism. Next, we extended the analysis to the KT transition in the 2d XY model.