Phase transition in an out-of-equilibrium monolayer of dipolar vibrated grains

We report an experimental study on the transition between a disordered liquidlike state and an ordered solidlike one, in a collection of magnetically interacting macroscopic grains. A monolayer of magnetized particles is vibrated vertically at a moderate density. At high excitation a disordered, liquidlike state is observed. When the driving dimensionless acceleration Γ is quasistatically reduced, clusters of ordered grains grow below a critical value, Γ(c). These clusters have a well-defined hexagonal and compact structure. If the driving is subsequently increased, these clusters remain stable up to a higher critical value, Γ(l). Thus, the solid-liquid transition exhibits a hysteresis cycle. However, the lower onset Γ(c) is not well defined as it depends strongly on the acceleration ramp speed and also on the magnetic interaction strength. Metastability is observed when the driving is rapidly quenched from high acceleration, Γ>Γ(l), to a low final excitation, Γ(q). After this quench, solid clusters nucleate after a time lag, τ(o), either immediately (τ(o)=0) or after some time lag (τ(o)>0) that can vary from seconds up to several hundreds of seconds. The immediate growth occurs below a particular acceleration value, Γ(s) (~/<Γ(c)). In all cases, for t≥τ(o) a solid cluster's temporal growth can be phenomenologically described by a stretched exponential law. The evolution of the parameters of this law as a function of Γ(q) is presented and the values of fitted parameters are discussed.