Non-equilibrium crystallisation across a dynamical phase transition

Dynamical phase transitions are non-equilibrium phenomena characterised by the non-analytical behaviour of some physical quantity. These processes share many features with equilibrium transitions, first and foremost the concept of universality. A lot of interest has been attracted in recent years by a special class of dynamical transitions, called absorbing phase transitions. Many processes ranging from fluids percolating through a medium to the spread of epidemics can be studied in the framework of absorbing phase transitions. These systems exhibit a dynamical transition from an active phase, where the order parameter fluctuates around a non-zero value, to an inactive phase, where the system is trapped into an absorbing state with no activity at all. In this thesis we discuss the properties of a numerical model of two-dimensional monodisperse interacting particles that exhibits an absorbing phase transition at high densities. The main feature of our model is that particles self-organise on the sites of a hexagonal lattice in a specific region of parameter space. The aim of this dissertation is to investigate the interplay between crystallisation and the absorbing phase transition. We study the universality class of this model by measuring several quantities and estimating critical exponents. We then focus on the ordering transition and we discuss its similarities with equilibrium crystallisation. Finally, we show that the non-equilibrium protocol defining our model can generate two dimensional crystals with long-range translational order, which cannot exist at equilibrium.